{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p align=\"center\">\n",
    "    <img src=\"https://github.com/GeostatsGuy/GeostatsPy/blob/master/TCG_color_logo.png?raw=true\" width=\"220\" height=\"240\" />\n",
    "\n",
    "</p>\n",
    "\n",
    "## Machine Learning with Linear Regression\n",
    "\n",
    "#### Michael J. Pyrcz, Professor, University of Texas at Austin \n",
    "\n",
    "##### [Twitter](https://twitter.com/geostatsguy) | [GitHub](https://github.com/GeostatsGuy) | [Website](http://michaelpyrcz.com) | [GoogleScholar](https://scholar.google.com/citations?user=QVZ20eQAAAAJ&hl=en&oi=ao) | [Book](https://www.amazon.com/Geostatistical-Reservoir-Modeling-Michael-Pyrcz/dp/0199731446) | [YouTube](https://www.youtube.com/channel/UCLqEr-xV-ceHdXXXrTId5ig)  | [LinkedIn](https://www.linkedin.com/in/michael-pyrcz-61a648a1)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's a simple workflow, demonstration of linear regression for subsurface modeling workflows. This should help you get started with building subsurface models that data analytics and machine learning. Here's some basic details about linear regression. \n",
    "\n",
    "* I have a lecture on [Linear Regression](https://youtu.be/0fzbyhWiP84) as part of my [Machine Learning](https://www.youtube.com/playlist?list=PLG19vXLQHvSC2ZKFIkgVpI9fCjkN38kwf) course. Note, all recorded lectures, interactive and well-documented workflow demononstrations are available on my GitHub repository [GeostatsGuy's Python Numerical Demos](https://github.com/GeostatsGuy/PythonNumericalDemos). \n",
    "\n",
    "#### Linear Regression\n",
    "\n",
    "Linear regression for prediction.  Here are some key aspects of linear regression:\n",
    "\n",
    "**Parametric Model**\n",
    "\n",
    "* the fit model is a simple weighted linear additive model based on all the available features, $x_1,\\ldots,x_m$.\n",
    "\n",
    "* the general form of the multilinear regression model takes the form of $y = \\sum_{\\alpha = 1}^m b_{\\alpha} X_{\\alpha} + b_0$\n",
    "\n",
    "* the specific form of the linear regression model takes the form $y = b_1 x + b_0$\n",
    "\n",
    "**Least Squares**\n",
    "\n",
    "* least squares optimization is applied to select the model parameters, $b_1,\\ldots,b_m,b_0$ \n",
    "\n",
    "* we minize the error over the trainind data $\\sum_{i=1}^n (y_i - (\\sum_{\\alpha = 1}^m b_{\\alpha} x_{\\alpha} + b_0))^2$\n",
    "\n",
    "* this could be simplified as the sum of square error over the training data, $\\sum_{i=1}^n (\\Delta y_i)^2$\n",
    "\n",
    "**Assumptions**\n",
    "\n",
    "* **Error-free** - predictor variables are error free, not random variables \n",
    "* **Linearity** - response is linear combination of feature(s)\n",
    "* **Constant Variance** - error in response is constant over predictor(s) value\n",
    "* **Independence of Error** - error in response are uncorrelated with each other\n",
    "* **No multicollinearity** - none of the features are redundant with other features \n",
    "\n",
    "#### Other Resources\n",
    "\n",
    "This is a tutorial / demonstration of **Linear Regression**.  In $Python$, the $SciPy$ package, specifically the $Stats$ functions (https://docs.scipy.org/doc/scipy/reference/stats.html) provide excellent tools for efficient use of statistics.  \n",
    "I have previously provided this example in R and posted it on GitHub:\n",
    "\n",
    "* [Linear Regression in R](https://github.com/GeostatsGuy/geostatsr/blob/master/linear_regression_demo_v2.R)\n",
    "* [Linear Regression in R markdown](https://github.com/GeostatsGuy/geostatsr/blob/master/linear_regression_demo_v2.Rmd) with docs \n",
    "* [Linear Regression in R document](https://github.com/GeostatsGuy/geostatsr/blob/master/linear_regression_demo_v2.html) knit as an HTML document\n",
    "\n",
    "and also in Excel:\n",
    "\n",
    "* [Linear Regression in Excel](https://github.com/GeostatsGuy/ExcelNumericalDemos/blob/master/Linear_Regression_Demo_v2.xlsx)\n",
    "\n",
    "#### Workflow Goals\n",
    "\n",
    "Learn the basics of time series analysis in Python to for analysis, modeling and prediction with production data. This includes:\n",
    "\n",
    "* Basic Python workflows and data preparation\n",
    "\n",
    "* Training linear regression model parameters to training data\n",
    "\n",
    "* Model visualizaton and checking  \n",
    "\n",
    "#### Getting Started\n",
    "\n",
    "Here's the steps to get setup in Python with the GeostatsPy package:\n",
    "\n",
    "1. Install Anaconda 3 on your machine (https://www.anaconda.com/download/). \n",
    "2. From Anaconda Navigator (within Anaconda3 group), go to the environment tab, click on base (root) green arrow and open a terminal. \n",
    "3. In the terminal type: pip install geostatspy. \n",
    "4. Open Jupyter and in the top block get started by copy and pasting the code block below from this Jupyter Notebook to start using the geostatspy functionality. \n",
    "\n",
    "You may want to copy the data file to your working directory. They are available here:\n",
    "\n",
    "* Tabular data - [Density_Por_data.csv](https://raw.githubusercontent.com/GeostatsGuy/GeoDataSets/master/Density_Por_data.csv).\n",
    "\n",
    "or you can use the code below to load the data directly from my GitHub [GeoDataSets](https://github.com/GeostatsGuy/GeoDataSets) repository.\n",
    "\n",
    "#### Import Required Packages\n",
    "\n",
    "Let's import the GeostatsPy package."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "supress_warnings = False\n",
    "import os                                                   # to set current working directory \n",
    "import numpy as np                                          # arrays and matrix math\n",
    "import scipy.stats as st                                    # statistical methods\n",
    "import pandas as pd                                         # DataFrames\n",
    "import matplotlib.pyplot as plt                             # for plotting\n",
    "from matplotlib.ticker import (MultipleLocator, AutoMinorLocator) # control of axes ticks\n",
    "cmap = plt.cm.inferno                                       # default color bar, no bias and friendly for color vision defeciency\n",
    "plt.rc('axes', axisbelow=True)                              # grid behind plotting elements\n",
    "if supress_warnings == True:\n",
    "    import warnings                                         # supress any warnings for this demonstration\n",
    "    warnings.filterwarnings('ignore')  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you get a package import error, you may have to first install some of these packages. This can usually be accomplished by opening up a command window on Windows and then typing 'python -m pip install [package-name]'. More assistance is available with the respective package docs. \n",
    "\n",
    "#### Declare functions\n",
    "\n",
    "Let's define a couple of functions to streamline plotting correlation matrices and visualization of a decision tree regression model. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def add_grid():\n",
    "    plt.gca().grid(True, which='major',linewidth = 1.0); plt.gca().grid(True, which='minor',linewidth = 0.2) # add y grids\n",
    "    plt.gca().tick_params(which='major',length=7); plt.gca().tick_params(which='minor', length=4)\n",
    "    plt.gca().xaxis.set_minor_locator(AutoMinorLocator()); plt.gca().yaxis.set_minor_locator(AutoMinorLocator()) # turn on minor ticks   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Set the working directory\n",
    "\n",
    "I always like to do this so I don't lose files and to simplify subsequent read and writes (avoid including the full address each time).  Also, in this case make sure to place the required (see below) data file in this working directory.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "#os.chdir(\"C:\\PGE337\")                                       # set the working directory"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Loading Data\n",
    "\n",
    "Let's load the provided dataset. 'Density_Por_data.csv' is available at https://github.com/GeostatsGuy/GeoDataSets. It is a comma delimited file with 20 density measures ($\\frac{g}{cm^3}$) and porosity measures from 2 rock units from the subsurface, porosity (as a fraction). We load it with the pandas 'read_csv' function into a data frame we called 'df' and then preview it by printing a slice and by utilizing the 'head' DataFrame member function (with a nice and clean format, see below).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Density</th>\n",
       "      <th>Porosity</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.281391</td>\n",
       "      <td>16.610982</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.404932</td>\n",
       "      <td>13.668073</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2.346926</td>\n",
       "      <td>9.590092</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.348847</td>\n",
       "      <td>15.877907</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2.331653</td>\n",
       "      <td>4.968240</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Density   Porosity\n",
       "0  1.281391  16.610982\n",
       "1  1.404932  13.668073\n",
       "2  2.346926   9.590092\n",
       "3  1.348847  15.877907\n",
       "4  2.331653   4.968240"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#df = pd.read_csv(\"Density_Por_data.csv\")                    # read a .csv file in as a DataFrame\n",
    "df = pd.read_csv(r\"https://raw.githubusercontent.com/GeostatsGuy/GeoDataSets/master/Density_Por_data.csv\") # load data from Dr. Pyrcz's GitHub repository\n",
    "df.head()                                                   # we could also use this command for a table preview "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is useful to review the summary statistics of our loaded DataFrame.  That can be accomplished with the 'describe' DataFrame member function.  We transpose to switch the axes for ease of visualization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>count</th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>min</th>\n",
       "      <th>25%</th>\n",
       "      <th>50%</th>\n",
       "      <th>75%</th>\n",
       "      <th>max</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Density</th>\n",
       "      <td>105.0</td>\n",
       "      <td>1.737917</td>\n",
       "      <td>0.288278</td>\n",
       "      <td>0.996736</td>\n",
       "      <td>1.552713</td>\n",
       "      <td>1.748788</td>\n",
       "      <td>1.906634</td>\n",
       "      <td>2.410560</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Porosity</th>\n",
       "      <td>105.0</td>\n",
       "      <td>12.531279</td>\n",
       "      <td>3.132269</td>\n",
       "      <td>4.966421</td>\n",
       "      <td>10.546483</td>\n",
       "      <td>12.411608</td>\n",
       "      <td>14.230930</td>\n",
       "      <td>20.964941</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          count       mean       std       min        25%        50%  \\\n",
       "Density   105.0   1.737917  0.288278  0.996736   1.552713   1.748788   \n",
       "Porosity  105.0  12.531279  3.132269  4.966421  10.546483  12.411608   \n",
       "\n",
       "                75%        max  \n",
       "Density    1.906634   2.410560  \n",
       "Porosity  14.230930  20.964941  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe().transpose()                                   # summary statistics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we extract:\n",
    "\n",
    "* the predictor feature, Density\n",
    "* response feature, Porosity \n",
    "\n",
    "from the DataFrame into separate ndarrays called 'X' and 'y' respectively for convenience."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "xname = 'Density'; xlabel = 'Density'; xunit = '$g/cm^3$'\n",
    "yname = 'Porosity'; ylabel = 'Porosity'; yunit = '$\\%$'\n",
    "xmin = 1.0; xmax = 2.4; ymin = 4.0; ymax = 22.0\n",
    "y = df[yname].values                                        # extract features are 1D ndarrays\n",
    "x = df[xname].values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Liner Regression Model\n",
    "\n",
    "Let's first calculate the linear regression model with SciPy package, stats module.\n",
    "\n",
    "* recall we imported the module as 'st' above\n",
    "\n",
    "````python\n",
    "import scipy.stats as st                                    # statistical methods\n",
    "````\n",
    "\n",
    "We instantiate and fit the model all in one line of code!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The model parameters are, slope (b1) = -9.1, and the intercept (b0) = 28.35\n"
     ]
    }
   ],
   "source": [
    "slope, intercept, r_value, p_value, std_err = st.linregress(x,y) # instantiate and fit a linear regression model\n",
    "\n",
    "print('The model parameters are, slope (b1) = ' + str(round(slope,2)) + ', and the intercept (b0) = ' + str(round(intercept,2)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that we have 5 outputs when we instantiate and fit our model.\n",
    "\n",
    "* **slope** - the slope of our linear model, the $b_1$ in the model, $y = b_1 x + b_0$\n",
    "* **intercept** - the intercept of our linear model, the $b_0$ in the model, $y = b_1 x + b_0$\n",
    "* **r_value** - the Pearson correlation, the square is the $r^2$, the variance explained\n",
    "* **p_value** - the p-value for the hypothesis test for the slope of the model of zero\n",
    "* **stderr** - the standard error of the slope parameter, $SE_{b_1}$\n",
    "\n",
    "Let's plot the data and the model, to get out estimates we substitute our predictor feature values into our model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_values = np.linspace(xmin,xmax,100)                       # return an array of density values \n",
    "y_model = slope * x_values + intercept                      # apply our linear regression model to estimate at the training data values\n",
    "\n",
    "plt.subplot(111)                                            # plot the model\n",
    "plt.plot(x, y, 'o', label='sample data', color = 'darkorange', alpha = 0.2, markeredgecolor = 'black',zorder=10)\n",
    "plt.plot(x_values, y_model, label='model', color = 'black',zorder=1)\n",
    "plt.title('Linear Regression Model, Regression of ' + yname + ' on ' + xname)\n",
    "plt.xlabel(xname + ' (' + xunit + ')')\n",
    "plt.ylabel(yname + ' (' + yunit + ')')\n",
    "plt.legend(); add_grid(); plt.xlim([xmin,xmax]); plt.ylim([ymin,ymax])\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=1.0, top=1.0, wspace=0.2, hspace=0.2); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The model looks reasonable. Let's go beyond occular inspection.\n",
    "\n",
    "#### Model Checking\n",
    "\n",
    "Let's test the slope with the following hypothesis test:\n",
    "\n",
    "\\begin{equation}\n",
    "H_0: b_{1} = 0.0\n",
    "\\end{equation}\n",
    "\n",
    "\\begin{equation}\n",
    "H_1: b_{1} \\ne 0.0\n",
    "\\end{equation}\n",
    "\n",
    "and see if we can reject this hypothesis, $H_{0}$ , that the slope parameter is equal to 0.0.  If we reject this null hypothesis, we show that the slope is meaning full and there is a linear relationship between density and porosity that we can use.\n",
    "\n",
    "Fortunately, the $linregress$ function from the $stats$ package provides us with the two sided p-value for this test.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Two-sided p-value for a hypothesis test whose null hypothesis is that the slope is zero = 7.744611355360021e-29.\n"
     ]
    }
   ],
   "source": [
    "print('Two-sided p-value for a hypothesis test whose null hypothesis is that the slope is zero = ' + str(p_value) + '.')      "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the demo case we reject the null hypothesis and adopt the alternative hypothesis, $H_1$, that the slope is not equal to 0.0.\n",
    "\n",
    "We can also observe correlation coefficient, $r$ value, and the $r^2$ value that indicates the proportion of variance that is described for our model. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The correlation coefficient is = -0.84 and the r-squared value =  0.7\n"
     ]
    }
   ],
   "source": [
    "print('The correlation coefficient is = ' + str(round(r_value,2)) + ' and the r-squared value = ', str(round(r_value**2,2)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Confidence Intervals\n",
    "\n",
    "Let's calculate the 95% confidence interval for the slope parameter, $b_1$ of our model.\n",
    "\n",
    "We first need the $t_{critical}$ value, given $\\alpha$ and $df = n-2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The t critical lower and upper values are [-1.98  1.98]\n",
      "and the t statistic is -15.58\n"
     ]
    }
   ],
   "source": [
    "alpha = 0.05\n",
    "t_critical = st.t.ppf([alpha/2,1-alpha/2], df=len(x)-2)\n",
    "print('The t critical lower and upper values are ' + str(np.round(t_critical,2)))\n",
    "print('and the t statistic is ' + str(round(slope/std_err,2)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see a consistent result with the previousl hypothesis, since the t statistic is outside the t critical lower and upper interval, we reject the null hypothesis, $h_0$, that the slope, $b_1$ is equal to 0.0.\n",
    "\n",
    "Next let's calculate the confidence interval of the slope.  We just need our t critical and the standard error in the slope."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The slope confidence interval is -9.1 +/- 1.16\n",
      "The slope P02.5 and P97.5 are [-10.26  -7.94]\n"
     ]
    }
   ],
   "source": [
    "print('The slope confidence interval is ' + str(round(slope,2)) + ' +/- ' + str(round(t_critical[1] * std_err,2)))\n",
    "CI_slope = slope + t_critical*std_err\n",
    "print('The slope P02.5 and P97.5 are ' + str(np.round(CI_slope,2)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Prediction\n",
    "\n",
    "Let's use this model to make a prediction at all the data locations.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_hat = slope * x + intercept\n",
    "plt.subplot(111)\n",
    "plt.hist(y_hat, color = 'darkorange', alpha = 0.8, edgecolor = 'black', bins = np.linspace(5,20,40))\n",
    "plt.xlabel(yname + ' (' + yunit + ')'); plt.ylabel('Frequency'); plt.title(yname + ' Predictions'); plt.xlim([ymin,ymax])\n",
    "add_grid()\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=1.0, top=1.0, wspace=0.2, hspace=0.2); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is useful to plot the predictions of porosity and porosity data vs. the density data. From this plot we can observe the linear limitation of our model and get a sense of the unexplained variance $\\frac{\\sum_{i=1}^{n}(y_i - \\hat{y}_i)^2} {n-1}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.subplot(111)\n",
    "plt.plot(x, y, 'o', label='training data', color = 'darkorange', alpha = 0.8, markeredgecolor = 'black')\n",
    "plt.plot(x, y_hat, 'o', label='model', color = 'black')\n",
    "plt.title('Comparison of Training Data vs. Model')\n",
    "plt.xlabel(xname + ' (' + xunit + ')')\n",
    "plt.ylabel(yname + ' (' + yunit + ')')\n",
    "plt.legend(); add_grid(); plt.xlim([xmin,xmax]); plt.ylim([ymin,ymax])\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=1.0, top=1.0, wspace=0.2, hspace=0.2); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next let's calculate the residual and check their distribution.  Residuals are the true values at the data locations minus the estimates at the data locations, $y_i - \\hat{y}_i$.  We want to make sure the average is close to 0.0 and to observe the shape and spread of the residual distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The average of the residuals is 0.0\n"
     ]
    }
   ],
   "source": [
    "residual = y - y_hat\n",
    "\n",
    "plt.subplot(111)\n",
    "plt.hist(residual, color = 'darkorange', alpha = 0.8, edgecolor = 'black', bins = np.linspace(-4,4,30))\n",
    "plt.title(\"Residual, Error at Training Data\"); plt.xlabel(yname + ' True - Estimate (%)');plt.ylabel('Frequency'); add_grid()\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=1.0, top=1.0, wspace=0.2, hspace=0.2); plt.show()\n",
    "\n",
    "print('The average of the residuals is ' + str(round(np.mean(residual),2)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we will check the cross validation plot, truth vs. estimated, and cross validation residual plot, residual vs. the fitted value.  \n",
    "\n",
    "* With these plots we check if the errors are consistent over the range of fitted values. \n",
    "\n",
    "* For example, we could use this plot to identify higher error or systematic under- or overestimation over a specific range of fitted values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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9x3rcX+MxdfVGzgVGYg23bovV0+frMX0BuE6sTPDNsS44u5/vP4wx52INqT0FGOPjPmtU0/84gT/n3401Muh81/96H9f2mv4vfwTeq/Y6tjLG/A1reH85tb/vqzDGFAMfYH0G3cThc34MVk/pDOB41+v1H2p+vfZR8/9Tre89O2hDM0wYq4t/IjBHrAQmLUSkmesqh9fMXMYafvcR8JBYk/bPwroy9CyAiNwoIu1dV/F+cz2sQkT6i8iZri+lu7CGLdQ2JGMB1klgOFWHBrR2PX6Pq9fpbz4+3UVYCSC6uz4876t2f2usK9z7RaQX1onI7WdXrF1q2Pd/gFPESq/fVKwkLt2xhskERV2vA9bVNYcEIFGOF58Dp4tIkljDwu6vdv9Waj5Wvnoe64rtDRweNuuecN7V1bjaiXUV3OehPd6IyPFiLTvQEusL6x6PfW7Faph5TdRRD3W9f6sfu7nAX109FSIiLcVK+NEa60tGOXCH6//2auoYpuS6Qr0YeAooNsZ86hFXOdZ7vamITMTqifDmW6C5K45mwASsYVlujwMPuL54IFYyp/Ta4lKqvvQ8VkVYnseMMWXAwxxuFNX4GeHHMV6E9dl3kliJlqqPblkD/J/rvdCTqhm3W2N91u/A+vL84NE+Ry/+i/XlfKwrhn5Yw5DdI5QCcZ6cCgx3Xeyt8VwhIqeKyCWuxsV+rB43b8d0MXCliFzsOudNpup39jXA5SIS56rzLo/73I20nwHEWs7Gn6Q9/8FqBE8G/u3uCRaR81zPqRlWQ3d/DbH7pab/cer+P/FXa6zj/ZtYCa+q/89Wfx+8gfV/eJPrfdPMdQxOc12Efxm43/U51x1rPmRdnsG6AHARrp5irHnDMbgaryKSBtS2hMsa4HqxRgOkUnX4b23fU2yhDc0wYqy5WKOwviz+jHVlYiRW1ryaXId1BfAnrCGN93kMHUkFvhCRPcBM4P+MNZ+jI9aH2C6sYTLvYXXp1xSXE+uLQEusK7Ruo7FOnrux3tz/9vF55mNN+H8Ha+jlO9WK3AZMFpHdWCfDRR6P3Yc1rn65WMMCqow7N8bswLrqejfWiWsscKUxZrsvsR2F2l6HF12/d4jIKgCxFmbOP9pKjTHfYp0M3sKag1F9seD5WHNBfhORV+tZx3+xTionYs13cOvmqncPVkPrMWPMMqjMXPf36vvycKIcuY7mH7E+k0ZhHcdfsD5A3V/83gG+ALaISCBez7rev/cDz7iO3RBXQ3A41tChX7Heu3+Gyi9vV7tu/4LVMH/ZhxiewTqhL/DYVggUYDUii7FO5j8e+dDKL/a3Yc1p24T1OnlmoZ2J9T9b5Pp/+hhriJdSQaHnsUrhfB57EogXkYHU/hnh6zGei/W59TmwiiM/+7KwEp38CkzC44Il1mdfMdbn15eu+gPK9fk8EEjDGkL9GDDUGPO1q8gR50kReVxEHvejjnVYQzHH1HauwGpQTHXFsQWrF+8eL/v7Aiv53vNYvZu/UvWzfSHW8XZizef7t8djv8S6mLACq/F0JlZWXF+fywGs1/Ayqr5WbbBe61+xXrMdWFNofP1O83m1c/6jru1e/8fr+j+ph0exkmdtx3qfFVS7fybW/ORfReQfrtFbyVjDiH/Cer3cyRjB+lxr5dr+NNZF47q8hJUw623jmt/qqucOrM+IX7E+j16vcQ9W0quBWI3yG/D4bK3jvWcLMT7n7lBKKaWUUkoppeqmPZpKKaWUUkoppQIqaA1NEeksVsa1L8VaHPdO1/bpIvK1WIvFvyIibYMVg1JKKaWUUkqp0Ava0FkROQFrIddVrkmon2FlojsJeMcYUy4i0wCMMeOCEoRSSimllFJKqZALWo+msRZaX+X6ezfWRPJOxpgic3gx54+xGp5KKaWUUkoppRqIkMzRFGuh93OwUkx7uoWqWSyVUkoppZRSSkW4psGuQERaYaXzvcsYs8tj+71Ya8U95+UxI4AR3vbXvHnzczt16hSkaJVSSkWafXv3Ur5lC22AH2C7Maa93TFFAtfyFgPdt2NjY4f/7ne/q/Nx7ik3InWv/+5rWX/2CbBr1y7atKlpedn67TdYZUHjjaRYg1kWGma8kRRrMGNoyPGuXr26fudWY0zQfoBmWGsrjaq2/c9Y6/u08HefJ598svHFvn37zL59+2wta4wxr776qq0xRFK8kRSrv2WN0XgjKdZgljWmYcZrV6xPPPGEuUfELABz27XXGuBTE8TzWkP+sfP8qv9DwY3B7ngjKdZgljWmYcYbSbEGM4aGHG99z63BzDorWIvgfmWMecRjeyrW4sODjLUYq1JKKeUXYwxZ48fzl7/8haXGUHzPPcx+4QW7w1JKKaWUSzCHzl4E3ASsE5E1rm1/B/4BxABLXV21Hxtj/hrEOJRSSjUgZWVl3HnDDVy8eDG9oqIYkZfHsGHD7A5LKaWUUh6C1tA0xnwIeBv0+59g1amUUqph27lzJxmXX86Qjz4iPzqa+195hbTLL7c7LKWUUkpVE5Kss0oppdTR2rhxI7179+a0jz7i323bMnzFCm1kKqWUUmEq6FlnlVJKqaO1du1aplx6KVu2b+fZU08lv6AAh8Nhd1hKKaWUqoE2NJVSSoW1Ze+8w2uDB/Pn/fuRnj35Z2EhcXFxdoellFJKqVpEZEOztLS0zjL79+/3eX/BKuum8fpWNpJi9besW2OON5JiDWZZt4YWb7Dqf+aZZ/g2I4NLKipYfMUVPL5wIc2bN/fp+CmllFLKPmHf0Ky+oHTHjh1tjEYppVQoGGOY8dBD3DdlCucATf/2N2ZNn05UlKYWUEoppSJB2Dc0jTFLgCXu2127dh0eGxvr8+O1bOSVtbt+LRvcsnbXr2WDWzYQ+ywvL2f0sGGcvWABFwN/ePhhRo0a5fN+lVJKKWW/sG9oKqWUajz27NlDxqBBXLVsGe81bUrGggWkX3WV3WEppZRSyk86BkkppVRY2Lp1K/369SNh2TJebdWKa99/XxuZSgVQYUE+QwZeQq8zExky8BIKC/LtDkkp1YBpj6ZSSinbffPNN0zs35+fNm/mucRE8gsKOOWUUzTpj1IBsrSoiHk5o5iYEk3S4DjWFG9mcvZIYDYpqWl2h6eUaoC0R1MppZStli9fzrRzz+XmzZu5+MwzWfHxx5xyyil2h6VUg7IgL5eJKdH07NKSpk2Enl1aMjElmvlzptsdmlKqgdKGplJKKdssXryY5/v148q9e/nXZZfx1IoVdOjQwe6wlGpwip1OkhJaVNmWlNACp9NpT0BKqQZPG5pKKaVsMXPGDIZccw3Ly8v58JZbmJefT8uWLe0OS6kGKcHhYE3xvirb1hTvw+Fw2BOQUqrB0zmaSinVQBUW5DN/znSczg04HIkMyxgTFnOxKioquH/UKLrl5XEpcOlDDzFu3DhExO7QGj1f5sTu37/f5/35WtaffbrZFau/Zd3sjvf/bs5g0sPjyEo1JMXHsqaklOyCMoaPv9NrbIGMt6EfW381tHgjKdZgxtAY4vVXRDY0I+1F0Xj1i4ZbY443kmINZlm3YMe7tKiIuVMzyUqNJunqtqwp+YnsSRkcOJBL7z59Ah6vr7GWlpaS+X//xxVLl/JpVBQ3zJ3LtdddV+PjQ3EibKxEZCAw0H27Y8eONkajgu3SSy8julkuOXm5FL/oJCHBwfDxmQxITrY7NKVUAxX2DU09ESqllP8W5OWSlRpNz0RrTlbPxBZkpUJOXv0amoGwY8cOrrnmGvp8/DGFsbFc8/LL9O3b15ZYFBhjlgBL3Le7du06PDY21ufHB6Os3fU39LKD0tMZlJ5uWwzhcAy0bPDK2l2/lg1+WX+FfUMzHE+EWja4Ze2uX8sGt6zd9TeWsiUlxfQYEkdU1OHhqD0cLSlZXELz5s2DFkNN5davX8+4fv3Y9OOPPN+pE6+8+io9e/YMeP1KKeUPb1MM+vTtZ3dYSjUImgxIKaUaIIcjMWwSf6xcuZL7evRg+I8/0qtbN5a9+y6nn356yONQSilPhQX5zMkeydjzNvPR6DjGnreZOdkjWVpUZHdoSjUI2tBUSqkGaFjGGCYXlvHp+r2UHzJ8un4vkwvLGJYxJqRxvPnmm+RdfDHX7NzJwosv5slPP6VTp04hjUEppbyZP2e617VFF+Tl2h2aUg1C2A+dVUop5T8ru+xscuZMx/miE4fDQUaWlXXWl0REgTD38cf52223cZoxRF97LU8uXEizZs1CVr9SStXG6dxA0uC4KtuSElpQvMhpT0BKNTDa0FRKqQYqJTXNluVMjDFMGjeOY6dP53LgnIkTuf/++3X5EqVUWLGmGGymZ5fD6/euKd5HQoLDvqCUakB06KxSSqmAKSsr47YhQ+g2fTrbRLgqL49JkyZpI1MpFXZqmmIwdESm3aEp1SBoj6ZSSqmA2LlzJzfeeCNnvP02H0ZHM+iVV0i7/HK7w1JKKa9qmmKgWWeVCgxtaCqllDpqGzdu5N60NJw//MD/OnTgP/n59OjRw+6wlFKqVt6mGOg8cqUCIyIbmr58AOzfv9/n/QWrrJvG61vZSIrV37JujTneSIo1mGXdGlK869atIzctjeG//MITCQlMKSggISGhxscEO1allFJK2S/sG5oiMhAY6L7dsWNHG6NRSinladmyZfx78GBuKi1lblISM994g7i4uLofqJRSSqkGLewbmsaYJcAS9+2uXbsOj42N9fnxWjbyytpdv5YNblm769eygSu78JlnGDZsGF0PHaLJFVfwxMKFtGvXLmT1K6WUUip8adZZpZRSfjHGMPX++9n65z9z1aFDXH733cz6979p3ry53aEppZRSKkyEfY+mUkqp8FFeXs7oYcNIWrCAH4G+ublk3HWXJs9QSimlVBXa0FRKKeWTPXv2cO2119L5P/9hddOm9Pv3v/nD1VfbHZbyICJNgE+BTcaYK+2ORymlVOOlDU2llFJ12rp1K3dccgnrv/yS/8bFseSNN7jwwgvtDksd6U7gK6CN3YEopZRq3II2R1NEOovIMhH5UkS+EJE7XdvjRGSpiHzn+u175gillFIht2nTJu5ISmL4l19yxokn8tGKFdrIDEMichJwBTDP7liUUkqpYPZolgN3G2NWiUhr4DMRWQr8GXjbGDNVRMYD44FxQYxDKaVUPS1fvpx3R4/mltJS5p15JnPeeosOHTrYHZby7lFgLNC6pgIiMgIY4e2+9u3b89prrwUnsiCIpFhB4w2mSIoVNN5giqRYIfLi9VfQGprGmM3AZtffu0XkK6ATkA70cxV7BngXbWgqpVTYWbxoEUNvuomTysr412WXMf/VV2nZsqXdYSkvRORKYJsx5jMR6VdTOWNMHpDn7b6uXbua9PT0OutyJ37yZckZX8v6s0+wvpzZFau/ZUHjjaRYg1kWGma8kRRrMGNo6PHWR0jmaIqIAzgH+C9wvKsRCrAFON5L+QZzxRUi72pFJMUbSbGCxhtMkRQrhH+8b77yConPPMNg4OfUVAYNH85bb71ld1iqZhcBg0TkcqA50EZEnjXG3GhzXEoppRqpoDc0RaQV8BJwlzFml4hU3meMMSJiqj8mXK+4+lsWIu9qhZ3xRlKs/pYFjTeSYg1mWQjveCsqKvj7yJH0fOYZfgPOzM6m2xlncNVVV4VdrOowY8w9wD0Arh7N0drIVEopZaegJQMCEJFmWI3M54wxL7s2bxWRE1z3nwBsC2YMSimlfFNaWsqQIUPY/M9/8l1UFCctXMiYCRPwvEColFJKKeWLoPVoivXNZD7wlTHmEY+7Xgf+BEx1/Q7v8WNKKdUI7Nixg4wBA/h29WpK2rThlVdfpX///naHperBGPMuVv4DpZRSyjbB7NG8CLgJuERE1rh+LsdqYA4Qke+Ay1y3lVJK2WT9+vXcds453Lp6Nd3bt+fD5cu1kamUUkqpoxLMrLMfAjWNt7o0WPUqpRqf1as+47l5M3E6N+BwJDIsYwwpqWl2hxURVq5cyfQBA7h1507yunUjd9kyOnXqZHdYSimllIpwIck6q5RSwVJYkM8Hr+Ux7ep2JA2OY03xZiZnjwRma2OzDm++8QbXDRnCcaWlxFx8MfPefJM2bdrYHZZSSimlGoCgJgNSSqlgmz9nOhOSm9KzS0uaNhF6dmnJxJRo5s+ZbndoYe3JvDw+GTSI60pL6fOnP/HkO+9oI1MppZRSAaMNTaVURHM6N3Bmp5gq25ISWuB0Ou0JKMwZY5jy979TcdddxBlD53vu4amnnqJZs2Z2h6aUUkqpBiQih86611Wrzf79+33eX7DKumm8vpWNpFj9LevWmOMNVqzx8Qms2/Q9fdtVVG5b5dxHfHz8EfE31GPra9mysjL+9re/Uf7CC0SJ0GnWLEbccotPj60r3nA6tkoppZSyX9j3aIrIQBHJc//s3bvX7pCUUmFk6IhMphSV8+mGfZQfMny6YR/ZBWUMHZFpSzxLi4q4aXAafXqexk2D01haVGRLHNXt3LmT21JT+fqFF/hPixac+cIL/OmWW+wOSymllFINVNj3aBpjlgBL3Le7du06PDY21ufHa9nIK2t3/Vo2uGUDvc9B6emsWvUZMz79EOdiJw6Hg5H31Z51NljH4P333mVezigmpkSTNORY1hRvZXLOKGJijkxMFMrXYePGjdzdvz/Dvv+ep9u2Zfabb3LOOedExOtbn7JKKaWUsl/YNzSVUqou5/Q4l/snTbY7DObPmc7ElGh6dmkJ4EpMBDlzptuWAXft2rVMuvRS/rp9O3MTEsh5912OP/54W2JRSimlVOMR9kNnlVIqUjidG0hKaFFlm52Jid5+6y36XXwxK7dv56mePXl81SocDoctsSillIo8q1d9xpCBl9DrzESGDLyEwoJ8u0NSEUQbmkopFSAORyJrivdV2bameJ8tjbuFzzzD0pQUhu7ezYVDhvDkBx8QFxcX8jiUUkpFJvc61WPP28xHo+MYe95m5mSP1Mam8pkOnVVKRbzVqz7juXkzcTo34HAkMiyj9jmawTIsYwyTs0cyMcXqyVxTvI/JhWVkZI0JWQzGGKZNmkTTSZNwACW3384Ljz5KVJReV1R106zjgS/r1pjjjaRYg1nWLVLinTtrGhOSm9LDEQsYejhimZBsyJk1jT59+4VVrG6RcmzdIi1ef2lDUykV0dxXXKdd3Y6kwXGsKd7M5OyRwJEJeILNqm82OXOm43zRSkyUkRW6Rm95eTl/+ctf2DJ3Lr2A2NxcHrzrrpDUrSKPiAwEBrpvd+zY0cZolFLhptjp5MzkautUx8dS/KLTnoBUxNGGplIqos2fM50JyU3DJgFPSmqaLfXu2bOHzMGD+fb991kXE8PNzz/PH66+OuRxqMgRjlnd7a5fywa3rN31a1n/yiZ26cK6Td/S/9jDI2LWOveSmNjF6+Mj5Xlp2fqX9VdENjQjrZtZ49WhU26NOd5gxbph/XrOvCyGioqKym1ndW7OhkXrj4i/oR7brVu3Mjo1leHffMOzrVuT8/rrnH/++TXWEYx4w+nYKqWUOnrDMsYwZfzNtG6117bpICqyhX1DU4f2KKVqk+BwsG7T9/Rtd3jbmpJSEhIctsUUSt9++y33p6Zy25Yt5HXsSFZhId26dbM7LKWUUhEuJTWNFStGkLPyQ1umg6jIF/YNzXAc2qNlg1vW7vq1bHDLBnqfw28f57riWlp5xXVK0UEyssbV+Hi7j0Ggyi5fvpw/DBxIk19/pdnppzPjzTdJSEgIaQyh2Ke/ZZVSSgVGuKxTrSJT2Dc0lVKqNo31iuviRYv46PrrGXboEF8MHMhjTz5Jy5Yt7Q5LKaWUUgrQhqZSqgFobFdcZ06fzr6xYzkD+N8tt/DyE09w8OBBu8NSSimllKqkC6sppVSEqKioIDMzkzfGjqUJsCM7m4fnzaNpU71mqJRSSqnwot9OlFIqApSWlnL7Ndfw5Ztv8mmzZtz85JNcf+ONdoellFJKKeWVNjSVUirM7dixg4wBAxi6ejWHYmN54M036d+/v91hKaWUUkrVSIfOKqWUS2FBPkMGXkKvMxO5aXAaS4uK7A6JDRs2MKxHD4atXs3C9u25+5NPtJGplFJKqbCnPZpKKYXVyJyTPZKJKdEkDY5jlXML2VMziYmJti2D7aeffsq1f/wjB3/+mWbduvHosmV06tTJlliUUkoppfwRkQ3N0tLSOsvs37/f5/0Fq6ybxutb2UiK1d+ybo053nCPde6saUxIbkYPRyxg6JEQy73JhhmzptGnb79677cmdcX7nzffZNkNN/CXsjI+uPRSZj/3HG3atKnxcXYf33B63yqllFLKfmHf0BSRgcBA9+2OHTvaGI1SqqEqdjpJGtyuyrak+FiKX3KGPJb5TzzBz6NGcb4xfHD11bz81FM0a9Ys5HEopZRSStVX2Dc0jTFLgCXu2127dh0eGxvr8+O1bOSVtbt+LRvcsnbXX1PZxC5dWPvjZnp2aenaUsHa4lISE7uE7LkZY5gwYQLvP/ggg4HvR4/m0UmTaNGixVHtN5Rl7a5fKaWUUuFBkwEppRQwLGMMkwvL+HT9XsoPGT7dsI/sgjKGZYwJSf1lZWXcNmQI7z/4ICuaNKFVXh7jJ09GREJSv1JKKeWpsCCfmQ9l0evMRIYMvITCgny7Q1IRJux7NJVSKhSshD+zyZkzHeeLTuLj4xk+PjMkiYB27tzJyMsvZ8hHH1ERHc3fX32VtLQ0n+adKqWUUoHmTpCX1ecAvU8/njXFm5mcPRKYbVuCPBV5tKGplLJFYUE+8+dMx+ncgMORyLCMMbafvFJS0ypjCFUjb+PGjdx+ySX87bvveKZtW+5++2169OgRkrqVUkopb+bPmc7ElGi6xglNmwg9u7RkYgrkzJlu+7laRQ5taCqlQq76UiKN9Urp2rVruTItjd0//USUw8HDy5bhcDjsDks1Ypp1PPBl3RpzvJEUazDLukVCvBvWr+esq9uxb+9BKioqADirc3M2LFp/RPx2x+opEo6tp0iL119Bm6MpIk+KyDYR+Z/HtiQR+VhE1ojIpyLSK1j1K6XCl/tKac8uLT2ulEYzf850u0MLmbffeovZ559Pxk8/cWbv3sz97DNtZKqQEpGBIpLn/tm7d6/dISmljtLSoiJuGpxGn56ncdPgNJYWFdVrPwkOB2tKqjaC1pSUkpDgCECUqrEIZo/m08BsYIHHthxgkjEmX0Qud93uF8QYlFJhyOncQNLguCrbkhJa4HzRaU9AIfbuO+8QM3s2l1ZU8PagQRT9+980b97c7rBUIxOOWd3trl/LBres3fU39LLvv/cu83JGWaOFhhzLmuKtTM4ZRUzMkaOF6trv8NvHMSV7JJkXHaD36cewpngfU4oOkpE1rsbHhsMx0LLBLeuvoPVoGmPeB36pvhlo4/r7GOCnYNWvlApfDkcia4r3Vdm2pnhfg+/RM8bwwAMP8OE//kFCRQVrb7+dx195RRuZSimljlogRwulpKaRkTWb7Pfj+P2MX8lZeQIZWY1reos6eqGeo3kXUCgiM7Aaub8Pcf1KqTAwLGMMk7NHMjHF6slcU7yPyYVlZGSFZikRO5SXlzN62DDWLFjAZyIMzc3lgTvvtDsspZRSDUSgRwulpKax/0AZ6enpAYhONUahbmj+Dcg0xrwkIkOA+cBl1QuJyAhghLcdtG/fntdeey24UQaYxhs8kRQraLyeelx2A2P/8yrbft5Ih/bH0yflGvYfKKt3neF8bEtLS1n44IPcum4d5U2acOGYMcQ7HGEdc3WRFKtSSjVG1mihzfTs0rJyW2MYLaTCV6gbmn8C3JfwXwTmeStkjMkD8rzd17VrV+PLlRV3Fidfxh0HqyxYX840Xt/KRlKs/pYFjbd6ufT0dJg0OSxjDWTZrVu38rdLL+WOL77g+Vat+GtREdu2bQvbeL3x5fiGS6xKKdVYNcbRQiq8hbqh+RPQF3gXuAT4LsT1K6VUyHzzzTdckZrKNqcTTjyRqcuWccopp2jvoFJKqYCz5k/OJmfOdJwvOnE4HGRk2b9GtWq8gtbQFJEXsDLKHiciG4H7gOHATBFpCuynhuGxSikV6ZYvX878lBRG7t3LC7168fiSJXTo0MHusJRSStVhaVERC/JyKSkpxuFIZFhG5DTWUlLTIiZW1fAFraFpjLmuhrvODVadSikVDhYvWsRH11/PlYcO8fpll/HOq6/SsmXLuh+oGjQRaQ5cCfQGTgRKgf8BbxpjvrAzNqWUpbAgn7lTM8lKjabHkDjWFG9mcvZIQDOuKuWvoC1vopRSjVFubi7Z117LaYcO8eEttzAvP18bmQoRmQQsBy4E/gs8ASwCyoGpIrJURM6yMUSlFNYSIVmp0fRMbHHUS4Qo1diFeo6mUko1SBUVFYzPyOCTxx5jLbDjgQd4+J57EBG7Q1Ph4RNjzH013PeIiHQA4kMZkKoqkodLqsBxOjeQdHXbKtuOZokQpRozbWgqpdRRKi0t5e4bbiCtoIBDUVHcunAh119/vd1hqTBijHmz+jbXUNpoY8wuY8w2YFvoI1MAD0yZzOtPPsTdfco5+9zmbN5fziM6XLJRcjgSWVPyEz0TW1Ru0yVClKqfiGxoutPd12b//v0+7y9YZd00Xt/KRlKs/pZ1a8zxRlKs/pTdsWMHI6+8khGff87LsbEMfvll+vbtW2c8De29EE6xRgIRuRUYDDQRkU+NMffYHVNjVViQz8LHHmLu4ENc1KUZpWXlRFVsY9RFHXhsznRtaDYywzLGkD0pg6xU6OFoqUuEKHUUwr6hKSIDgYHu2x07drQxGqWUOmzDhg1cnZ5Oyfffw3HHMSE/n9NPP93usFQYEpFBxpjXPTZdZoxJdd33OaANTZvMnzOdmKhDXOBoggi0jInixDZQsec3nE6n3eGpEEtJTePAgVxy8nIpWVyiS4QodRTCvqFpjFkCLHHf7tq163B/Fu7WspFX1u76tWxwy9pdf6DKrly5klkDBnDnzp3884wzmPHKK3Tt2jWkMYRjWbvrD2Nnisgw4D5jzBpgrYjMAwygGWdt5HRu4JSOMazZdJCe8dac6hYxUaz9cr8Ol2ykBiQnMyA5uSF87ihlq7BvaCqlVLh5Y8kSCgYPZnBZGYsuvpilixfTpk0bu8NSYcwY84CIdAQmi5UhKgtoDcQaY9baG13j5nAk0rtdOdlLt5E1oIJzOkWxwnmIGe83ZfJjOlxSKaXqS5c3USpCFBbkM2TgJfQ6M5EhAy+hsCDf7pAapSeeeILR6en0LCuj8Npreeqdd7SRqXy1F7gLmA3kAdcB39oZkLLm5C39IZrLzm7PtPeace4j5QxfHMWgW+7R4ZJhrrAgn5kPZel5UakwpT2aSkWAwoJ85mSPZGJKNEmDDy8gfeDAIwxITrY7vEbBGMOkceNYPn063wDOrCxmT5qEiFBeXm53eCrMicgUoBfWefd1Y8wgERkE/EdEnjbGLLA3QktjTAbXp28/Dhx4hKcen8GPpSV0OzuRoSMyGZCcXGMdkZSwzN+ybuGeDG5pURFzp2aS1aeMi05rz5qSn8ielMGBA7lez4sN9dgGs6xbJCWDa2jHNpgxhCLZnvZoKhUB5s+ZzsSUaHp2aVllAekFebl2h+aTwoJ8bhqcRp+ep0XkVeeysjJuGzKEbtOnc74I8+bO5f7Jk4O6RmakHzN1hCuNMcnApcBQAFdyoGSgnR0BichAEclz/+zdu9eOMMLCgORknnz+dZZ+uIaFi/P1Al4EWJCXS1ZqNOfEN7fOi4ktyEoN/HlxaVFR5WfxTYPTWFpUFND9K9WQaY+mUhHA6dxA0uC4KtuSElpQvMhpT0B+cPfGTkhuRtLgdqz90eqNjZT16Xbu3MmIK67gxuXL+U90NINeeYW0yy8Pap2RfsyUV/8TkTwgFnjPvdEYUw7MtCOgcEy2Z3f9Wja4ZQO5z5KSYnoMiWPP7p1ERVn9Jj0cLSlZXFLrY/2J4f333mVezihrNNGQY1lTvJXJOaOIiTnys9juYxsOZe2uX8sGv6y/tEdTqQjgcCSypnhflW1riveRkOCwJyA/VPbGJrao0hs7f850u0Or08aNG+l78cW8tnw589u1Y/iKFUFvZEJkHzPlnTHmRmAW8IAxJtPueJSKdDWdFwOZKbim0UT6WayUb7ShqVQEGJYxhsmFZXy6fi/lhwyfrt/L5MIyho4I/++rTucGkhJaVNmWlNAi7NenW7duHRMvuIDb//c/Ek89lUdXraJHjx4hqTtSj5mqmYhcbIxZZ4z5uob724jIGaGOS6lgqJ68LhjDTd3nxdUl+6ucF4dlBC5TsH4WK3V0InLobKRNnNV4wz8ZRLDLutU3Xneyiql5uRQvcpKQ4ODWsZn07tMn7I9vfHwCq5xb6JHgHppRwSrnPuLj40OaaGNpUZGV7KOkBIfjcLIPb5a98w6vDh7Mjfv3s7BHD956/XXi4uJCFm+wj1lDTwYRpv4oIjlAAfAZ8DPQHOgK9AcSgLvtC0+pwPCWvG7S1Ewgl0Hp6QGrxxq6Opuxo2/j56e/JEqgs+OUgO0f3L2mm+nZpWXltkD3mirVkIV9j6YmK1DKMiA5mYWL83l/5VcRlaxi6IhMsgvK+HTDPuuq84Z9ZBeEtjfWnZ1wXK9tfDiqHWN7bWHu1EyvV9mff/55bk9Pp8/+/byYlsY/33qLuLg4L3sNnnA4ZiqwXMNlrwQ2A9cA2cAooBvwhDGmjzFmpY0hKhUQ3oabBiNJj1ubpqUsHung25zuPHxFGXOyRx6RPK2+ydVqGk0UyF5TpRqysO/RDMdkBVo2uGXtrl/LBrbsoPR0YmKimTFrGsUvOUlM7MLI+8b4lNQmULE+O28m96XF0MNhlel1civuS9tLzryZlVfYjTFMmzSJZZMmsR747I47mPPgg7Rs2bLG/QYr3urH7Jg2x3CwIoYpE+7i2XmJDMuo+fjZ/V6wu/5wZoz5BZjr+lGqQfKavC4+luIXnQGva/6c6UxIblrZ42jNoYScOdMrPyOPJrmau9c0Z850nC86cTgcZGT5dv5SSkVAQ1MpFflSUtPo07cfYE+D4fAXH1O5LSmhBU7XF5/y8nJGDxtG0oIFXAxc+eij3DpiRMjj9OQ+ZkuLiqysh1dEk5RweA1VzUCrlApHXoeblpQGJXmd07mBMy+LqbLN87MdDvewui80emuM1iYlNU0/a5Wqp7AfOquUUkertuyEe/bs4U+pqfRdsIDVTZtyxksvcfudd9oU6ZEW5OVq1kOlVMTwNtw0WEP/HY5E1m06UGVb9TmUmtBHKftoQ1Mp1eBVfvFxz3lcv5fxr/zGj5u2cMJxcbz49tvMb9GC/3v/ff5w9dV2h1tFsdOpX5KUUhEjJTWNjKzZ5Kw8gd/P+JWclScwfHxuUPIKDMsYw5Si8lrnUIZiGRSllHc6dFYp1eBVzrOZNY3iF605j9t3HaTLtm/524FD3Nu2KfsS49i18ze7Qz1CgsPBmuKtmvWwgRCRFljZZeONMcNFpBtwqjHmDZtDUypgqg839SWDeX3rWbFiBDkrP6xxDuWwjDFMzh7JhGRDUnwsa51WYzQjSxP6KBVs2qOplLJN9bXWfM0EWB8pqWmVWXsrpAlJP/7CiD2H+M9JzflsSndyrmoVlsNRh47I1KyHDctTwAHgQtftTcAU+8JRKrKd0+NcFi15h0/WrWfRkneOmE9Z2cP6SUcuetjqYc3I0jnuSoWC9mgqpfxWWJDP/DnTcTo3EB+fwNARmX6vj+ZtrTV3kht34qBgeOWVV/j6o9XcCvzr9NbMv+tkWjZvQlyrplUSSISLAcnJxMRo1sMG5GRjzLUich2AMWafiIjdQSnVkNmdkE6pxioiG5qBWEQ+FGXdNF7fykZSrP6WdWsI8brXpMxKjSbp6rascm5mykNW8pza5uBUr3/urGlMSG7mygRo6OGIZUKyIWfWNHqdf0FAYq3u0Zwc3r//fjYDr5x7DM9lJNK0iVBRUcEq5z7i4+Mr9xNO74U+ffsd0fiu/ni74w2n922YKxMR600PiMjJWD2cSqlGrj4XcQsL8pk7axrFTieJXbrUuvyVUqEW9kNnRWSgiOS5f/bu3Wt3SEo1agvycslKjaZnYgsrC2piCyakxPi9GHex00lSfNUry0nxsRQXOwMYraWiooKsu+7i2Pvvpz8w9IYbKG3ajjUlpdZw1A37gpYVUalq7gcKgM4i8hzwNjDO1oiUUrZzj/IZe95mPhodx9heW5g7NbPWKSWVj+m1heWj2zH2vM3MyR4Z1GkoSvkj7Hs0jTFLgCXu2127dh0eDguCa9nglbW7fi1be9mSkmJ6DIkjKso92q+CHo4WlLxc4tO+3WUSu3Rh7Y9V11pb69xLYmIXmjdvHpBYweqJy7juOi5fsoSVUVGcPncuY2+5hcKCfGbMmY5zsTUcdeR93q8Ch+vrEK5l7a4/3BljikTkM+ACQIA7jTHbA7FvEekMLACOx+oxzTPGzAzEvpVSweVe79N9TuyZ2IKsVJhRy3qfR7tGqFLBFvYNTaVUeKlpMW5/s6C6MwFOTLGW61hTvC/gmQB37NjBVQMHsmLFCn5p2ZLbFi+mb9++gC7CrewhIm8bYy4F3vSy7WiVA3cbY1aJSGvgMxFZaoz5MgD7VkoFkdO5gaTBcVW2JcXH4lzs9OEx5vBjElqEZb4B1TiF/dBZpVR4OWIxbtewU3+zoHpbay2QmQDXr1/P3845h7+tWEHnk07iwY8/rmxkKhVqItJcROKA40SknYjEuX4cQKdA1GGM2WyMWeX6ezfwVaD2rZQKLq/rfdZxEVfXCFXhTns0lVJ+qVyT0pUFNT4+nuHjM+vVQAxWr+LKlSv5x4AB3LpzJ/O6dePDZcvo1KlT0NZyU8oHfwHuAk4EPsMaNguwC5gd6MpcDdhzgP9W2z4CGOHtMe3bt+e1114LdChBE0mxgsbrj9WrPuP9wlfZ9vNWOrQ/nj4pV3FOj3NrLN8Qjm33Hhcz7uU8JiTv5sxOMazbdIApReX0Th9S4/Or+THXBPSYRNLxjaRYIfLi9Zc2NJVSfvNsIIZb4+2NN97gb0OGML20lAUXX8y8N9+kTZs2doelGjnXXMmZInK7MWZWMOsSkVbAS8Bdxphd1eLIA/K8Pa5r164m3Ydlitz/877Mm/W1rD/7BOvLmV2x+lsWNF5/6n/9tdf4rOhZci6PISnhJNe0iue48MILvV6YbCjHNj09ncILL+Sfc6bjzHcSH9+VOyfVnnXW/Zg5s6ZR/B8niYmnMHZq7Vlng/FeCPdjG6oYGnq89RG0hqaIPAlcCWwzxpzhsf12IAM4BLxpjBkbrBiUUo1L3mOP8drIkWw0hsKhQ3lq3jyaNWtmd1hKVTLGzBKRM4DuQHOP7QsCsX8RaYbVyHzOGPNyIPap1NHwd/mNyszm7qQ4jSjBTX0u4uoaoSqcBXOO5tNAqucGEekPpANnG2NOB2YEsX6lVIgVFuQzZOAl9DozkSEDLwlZinVjDPePHcuBjAySjWHSvffy5NNPayNThR0RuQ+Y5frpD+QAgwK0bwHmA18ZYx4JxD6VOhr1WX7D69JXCS1wOp1BjlYpFWhBa2gaY94Hfqm2+W/AVGPMAVeZbcGqXykVWkesARai9bzKysrImzGDbtOns1WE1nl5TJwyBes7t1JhZzBwKbDFGHMzcDZwTID2fRFwE3CJiKxx/VweoH0r5bfKJTvc6y53acnElGjmz5le42MSHA7WlFTtzdMEN0pFplBnnT0F6C0i/xWR90TkvBDXr5QKEs81wHz9QnG0du7cyRVpaRQsX87CqCgWdT6Ogtdf0MWqVTgrNcZUAOUi0gbYBnQOxI6NMR8aY8QYc5YxJsn1859A7Fup+nA6N5CU0KLKtrp6J4eOyCS7wCOz+fq9TC70P7O5Usp+oU4G1BSIw1qo+jxgkYh0McYYz0INKSseRF5GqUiKN5JihYYd75dffoHjslb89tvBym2OYwxffvlFUJ739u3beXnCBG7dsoWPmwh/uOFY/tijNes2fcuU8TezYsWIWrMU2q0hvxdUrT4VkbbAXKzss3uAFbZGpFSQuNdd7uE4PBS2rt7JAcnJQC4582bifNGJw+EgI6v2eZ1KqfAU6obmRuBlV8PyExGpAI4DfvYsFK5Z8fwtC5GXUcrOeCMpVn/LQsOP97nup+PcubkygQPAp+v30r376aSnpwc01rVr1/LvYcO4a8cOHoyNIe+mtlzX+yQA+h8LrVvtJWflh9w/abJf+w1FWWiY74VwiTXcGWNuc/35uIgUAG2MMWvtjEmpYBmWMYbJ2SOZkGxIio9lrdPqnczIqr13ckBycq3ZVpVSkSHUQ2dfxUp+gIicAkQD20Mcg1INxtKiIm4anBby5DveDMsYw+TC4A93evvtt7n84ou5ascOnurZk50JHRjQvWWVMpo4QoUzETlLRAYBPYCuInK13TEpFQwpqWlkZM0m55OOXPTwr+SsPIGMrNnaO6kiml2JDyNRMJc3eQHoBxwnIhuB+4AngSdF5H9AGfCn6sNmlVK+KSzIZ+7UTLJSo+kxJI41xZuZnD0SsOckbtU5m5w504M23GnhM8+w6JZb2FRRwcvXXMPTCxYw9JrLWbfpW/ofe7icJo5Q4cq19NdZwBdAhWuzAXQpEtUg6fIbqiFxJz6cmBJN0uCq373c73N1WNAamsaY62q468Zg1alUYzJ/znRrrbHEFkRFCTt2l3Nw5xb+MvRqep1/YZ1rlQWD5xpggWSMYdqkSTSbNInLgdPvvJMHH3mEqKgohmWMYcr4m2ndai9JCS1ci3vXPTRLKZtcYIzpbncQSiml/OeZ+BCqrvOqDc0jhXrorFIqQJzODZVrjRV+vpM5hSVMTjnEkpsPhWxpkVAoLy/n9ltu4fhJk9gHVOTmMvXRR4mKsj6+UlLT6J0+gpyVJ/D7GTo0S4W9FSKiDU2llPJTOAxZrU8m5cZMG5pKRSiHI7FyrbH5725l4gCh+/FCi9jmIVlaJBT27NnDVYMG8djTT/NSs2ac8dJLZNx11xHlzulxLouWvMMn69azaMk72shU4WwBVmPzGxFZKyLrRESTASmlGizPBuJNg9NYWlRUr33YsVZ3dVYm5X1Vtul0nZppQ1OpCDUsY4y11tiGfWz4+QDdjoOfdlVwXPvjgci/wrZlyxaGnX8+Q/Pz6RQXx73vvccfrtacKSrizQduAlKBgcCVrt9KKdXgHNFA7LWFuVMz/W4g2rFWtzehSnzYUIR6eROlVICkpKZx4EAuOXm57CgtZtmGKPqffSLHHHMMENlX2L799lseTElh+NatzD3hBN5+911OOeUUu8NSKhB+Nsa8bncQSikVCkfMaUxsQVYqzJgz3a/RR07nBpIGx1XZlpTQAueLzkCGW6faEh+6l+NSh0VkQ9OXF3L//v0+7y9YZd00Xt/KRlKs/pZ1C3S8vfv0oXefPnzw/vvMnZrJiZ2akNTiEGtKSskuKGP4+Dsr67Q7Xl/LrVixgpv++Ece+e038k4/nelvvkmHDh3qjKWxvxfsjjecYg1zq0XkeWAJcMC90RijWWeVUg2O1wZifCzOxU6/9mMNWa26VrddF9SDlfiwIQr7hqaIDMRjWFHHjh1tjEap8DQgORmwejeLX3SSkOBg+PhM1/bI8cpLL/Gvm29mc3k5z6SksODZZ2nZsmXdD1QqcsRiNTA9/zl1eROlVIPktYFYUup3A3FYxhgmZ49kYgqaYT6ChH1D0xizBOvKLwBdu3Yd7s86TFo28sraXX+klh2Uns6g9HRbYziacjOnT2fv2LFcBcT/+c889I9/0Lp164DVX1iQz9xZ0yh2Okns0sXn5V/sPl6RVtbu+sOdMeZmu2OojY5oCXxZt8YcbyTFGsyybg0t3tr2eeOtdzJpaiZZqYak+FhWOfcxpfAAI+6506/99unbjwMHHmFqXi7Fi6wL6reOzaRP335V9tPQjm0wYwjFiKGwb2gqpRq2iooKxt15J11nz+YAsCM7m5xRoxCRgNXhTkYwIbkZSYPbsfbHwwss6/AXFQoiMtYYkyMis7B6MKswxtxhQ0w6YqgBWlpUxIK8XIqdThIcDoaOyKR3nz4hrzOcRtQsLSriqcdn8O0331BRfpAKacaZZ3QPuzgbouojrk7q3Jk/j76jXsd9QHKyvl4RRhuaSinblJaWMvTGG1n88sukNWnCjU8/zfU33hjwCfXuZAQ9HFavmOcCy9rQVCHylev3p7ZG4SEcRwzZXX+kly0syGdezigmpkSTNORY1hRvZXLOKOARBiQnByWGpUVFXuuMiTnyQp4dx8t9TDIvOkDHpN/YvlfIWQZ9j/2BeTXEaWe8kVy2pnKeI67c53e7Y9Wy9SvrL13eRCllix07dnDzRRcx5OWXOalNG8YsXcr1N94YlLp0gWVlN1ejDmCfMeYZzx9gX22PVcpXNS0BsSAvN2h1LsjLDYtlJ2riPibxsTuJbxdF75Obcl+y8MFXO8MqTqUaIp8amiLSTkROF5EuIqKNU6UauaNdfHn9+vXcds45DFu9mpfbtyd/+XL69+8fpGh1gWUVVu7xcZtSfqvpolpxsTNodRY7nWF9Ic99TA6UlREbbX2FTeoUhXP7gbCKU6mGqMZGo4gcIyJ/F5F1wMfAE8AioFhEXhSR4H0rVEqFraNdfHnlypX0ueACrvrxR+Z268aM1as544wzghpz5QLLG/bpAsvKFiKS5pqf2UlE/uHx8zRQbnN4qoGo6aJaQoIjaHUmOBxhfSHPfUxioqMpLasAYM2mChzHxYRVnEo1RLX1Ti4GfgR6G2NONcZcbIzpaYzpDEwF0kVkWEiiVEqFjSOGZiW2ICvVt+FH/3nzTR7o3ZvNP//M05ddxrxPP6VTp05BjzklNY2MrNnkfNKRix7+lZyVJ5CRpYmAVEj9hDU/cz/wmcfP60CKjXGpBqTyotr6vVUuqg0dkRm0OoeOyPRaZygv5HmOshky8JIqFz7dx6Sk9BhKfq3ggx/KmVRk6H3aMRFzwbG25xeI8koFS43JgIwxA2q5z32CtEWkpQLWeDW9vVtDiHfD+vWcdXU7KiqsK8MVFYazTmrOhhfX1/r8npgzh1/HjmWwMbQfMoSH586lWbNmXh8TjGPbp28/ep1/AQDNmzev8zH6XqjqaNLbh6psODPGfA58LiLPG2MOgjUtBehsjPnV3uhUQ2FdPJtNzpzpOF904nA4yMgaQ5++/YJW54DkZGJijqwzVBfyVq/6jFVvPWclIxocx5riqlnF3cdkzqxpfP31QXbv3oM5dJB1W7fT4fgTePC+8WSNuQ2HI9HnZa9CyT2KqKbnd7TllQomn7POikh74E6sxaYfN8Z8F7Soqtar6deVCiMJDgdrSrbQM/HwnJw1JaU1Ds0yxpCdlcWJjzxCHPDd6NHMnDQpoMuXKBVBlorIIKzz72fANhH5yBgTvC4n1agcblwdFuhM3r7UGSrvF75KzuXWKBvwnlU8JTWNPn37VcmQm9j2IO+tKeaJj4VxafF0OOZwgyyYDXN/eY4igrqzpvtbXqlg8md5k4eBuVjrfz0PnBeUiKoJx/TrWja4Ze2uX8vWXnb47eOYkj2SiSmlJCW0YFXxPh4oOsjI+8YdUb6srIxbb7mFhc89R2pUFOn/+AeTMjJCFquWDX1Zu+uPAMcYY3aJyK3AAmPMfSKy1u6gVGgUFuQzf850nM4NYduD5q+lRUU8O2+mbc9p289bSUo4qcq2pIQWOF90HlHWM0PuD99/S8rvmhLfzpDz/jYW3XlKZYMsnBqaTucGkgbHVdlW0/OrT3mlgqm2ZECFIuK5wm804HT9xAQ3LKUaH/ecij49T+OmwWkhmVNRn3kclfMdV57A72f8Ss4nHRk+PveILxY7d+5kWP/+XPncc3Ru0YK/vPQSf7rllmA9FaUiRVMROQEYArxhdzAqdI5IpHbeZuZkj4zo+XNLi4qYOzXT1ufUof3xPicj8syQW3bgAC1ioioz0EJ4Zct18zdrumZZV+GktmRAQ4CBIvKCiJwMZAEPATOB20IRnFKNhecXkOWj2zG215agn6yP5ktPSmoai5a8wyfr1rNwcT4DkpOr3L9x40ZG9OzJTR99xGtt2/LqBx+QkqL5TpQCJgOFwPfGmJUi0gUIyVQUZa+a1riM5HUcF+TlkpVq73Pqk3KVz8mIPDPkRsfEsO9ARWUGWgjPBllNCZ5qSmLkb3mlgqnGhqYxZqcxZgxwLzAF+Csw0hjzR2PMh6EKUKnGwFsm12CfrIP1pWft2rVcdP75DPr+e+YlJPDA6tX06NEjQFErFdmMMS8aY84yxtzmur3eGPNHu+NqSI52nd9gqWmNy3DrQfNHsdNJUnzVYe2hfk7n9Di36iibWrKKe2bIbRvXgcKvy7k3v4I/9+kQtg2yI0YR1ZE13d/ySgVTjXM0Xb2YfwPKgLuBk4F/i8ibwBxjzKHQhKhUw2fHnIpg1Pn2W28xOz2dn/btI+/ii3nltdeIi4ur+4FKNXAissgYM8T19zRjzDiP+4qMMck1P1r5qnrGzVXOLWRPzSQmJtr2L9rWkMbNlUlaIDx70PzhTg7X6+RWldvseE6+JiOqkiHX6aRN6+4cbA33F+3G4TihMltusJMn+cvfZEt2JmdSylNtQ2dfAF4GlgELjTEfGGNSgN+A8Lg8qFQDYcecikDXufCZZ1iaksL/7dvHTenpFC5dqo1MpQ7r5vF39eXD2ocykIbsaNb5DbaGOKRx6IhMsgsi6zl5Tv1466PPee+/n/PJuvUsWvKONs6UCrDaGpoxwAas5D+VYz2MMQuAK4MbllINS2FBPjMfyqox6c4RX0A27Av6yTpQX3qMMeQ89BBb//xnEioq+Pz225n38suVa1UqpQArY3t97lN+8Do8NT42LIanNsQhjQOSkxk+PrdBPSelVODUtrzJbcBsrKGzf/W8wxgTXmMKlApj7qFcWX0O0Pv0470unuy5yPaGRetJSHCQkTUuqCfrmhb29qfO8vJybs/I4MmnnyYZGJSby4N33VV5v2cq//j4BIaOyGRQenrAn4tSEaCFiJyDdYE31vW3uH4azNotdvM6PLWkNGyGpzbEIY0DkpP1c10p5VWNDU1jzHJgeQhj8ZkvY+f379/v8/6CVdZN4/WtbCTF6k/ZubOmkXnRAU5s9gvffv0z7aKjybzoGObMmlZlra4+ffvRp2+/yv02b968zud3tPG66/TkWWdt9e/Zs4fMwYMZ+P77LIuJ4eannyY9Pb3yMe6091mp0SRd3ZZVzs1MeehOgCOy1Fb35ptv8Nz8f7Cx5EcSHA6Gjsis8zGR8F7w1NDiDadYw9Rm4BHX31s8/nbfVgEwLGMMk7NHMjHFmnO+yrmP7IIyRt4XvkM5lVKqoaotGdAS4Amg0BhzsNp9XYA/A05jzJPBDFBEBgID3bc7duwYzOqUCrivv/6Kjmf9ygmtoVXzppSWHaSsbBtff32w7geHqS1btjD28su59euveb5VK/65eDF9+vSpUqYy7X2iNYytZ2ILJqTAjLzcWhuNS4uKeHrGGCakxNBjSDvWlFjJPKD2xykVzowx/e2OwReRfqGxT99+HDjwCFPzcile5OSkzp3509130KdvP9sultQWb6hisDveUMe6tKiIBXm5FDudlRcre1c7RwUqBm9lvdXvef5qaO+FSIo1mDE0hnj9VdvQ2eHAKGCmiPwC/Aw0BxzAD8BsY8xrwQ7QGLMEWOK+3bVr1+Gxsb6PMtKykVfW7voDXbaivIzte4Vu7YUoEVrGNGH7XkNFeVmtjw3X5/bNN9+QlpLCfcXFPHnCCdxbUEC3bt2OKFtSUkyPIXFERYlrSwU9HC0oebmk1hienTeTiWnN6ZnYgqioKHqd3Ir70vaSM29mrcOzwvV4NbaydtevfNdQL+QOSE6u/FLfgHrElY+qjKYZfPhiZdnBaVx66WW21a8XS1VjVNvQ2S3AWGCsiDiAE4BS4FtjzL6aHqdUIHjO7XM4EhmW4d/cwXBySKLJWbaPey+roGfnKNZsqiBnGRySGLtD89vy5cuZkZbGxt27+ed55/H6G2/QunVrr2XrO1fK6dxA0tVtq2wL9lIvSjVG4Xgh1+76g1HWnQzugQl3+Xw+i5Tn5m/ZUNT/7LyZ3JcWU3nucV+snPrUHK644sqgx1BT/Z4XS+1+HYJV1u76tWzwy/qrtqyzlYwxTmPMCmPMGm1kqmBzJ88Ze95mPhodx9jzNjMne+QRmVojxdlnnk7yOR3IebcJv591iJz3o0k+pwNnn9nd7tB84l78vFvn9izq3Zubdu/m2uRk3l62jA4dOtT4OG+ZdLML6s5q63Aksqak6lCSSF9rTinVOB1OBvdLgzifRQKvmYcTWlBc7LS1/nDIfKxUqPnU0FQqlI5YB61LSyamhMc6aPUxLGMMS3+I5vYBx/LR/WcwdmAnlv4QHdbrjLkVFuRz/6ib+d8nH/Dnjds52xjGHdOc6+64nZYtW9b62CNS+X/SkeHjc+u8kj8sY4y1LtuGfX4tu+JuENe0hIxS4UZE7rc7BhU8hQX5ZP7lem7qVsKJzX5h755dEX8+iwQ1rRGdkOCwtX69WKoaI21oqrDT0K4Guhtc2e/Hhe06YzU10h6YOI7NW7bx1bZylgFrfx9F4gnlTJt8r0/79VwYe+HifJ/mp6Skplnrsn3S0efjtXrVZw2qF1w1GoPsDkAFh7sns9mhvVx1VjNOaF3Ots0l7Ny5M6LPZ5GgpjWih47ItLX+SLi4rFSg1ZYM6KiIyJPAlcA2Y8wZ1e67G5gBtDfGbA9WDCoyeZ3bF+FXA1NS09h/oIz0eq41Fsw5q+4vRBNTokkaHFe5zueZfYew6fP/8WCZ4b4ouOWGaK4/tykrSw5x7bPfBqTumriTefg6b+D9wlfJuTy68j1j9RpAzpzpYdWgV6oaqbuIikTukTk5S5rz+aYykjpFcWIbYcvPW/luR9OIPp+Fu5rWiK6+lFeo69dzkWqM6mxoishFwP1Agqu8AMYY06WOhz4NzAYWVNtfZyAZKPE/XNUYVF8HbU3xPiYXlpGR1TiuBrrTopeUFONwJHL2+f34b/4zRzQEYXZATpyeQ5XBaqTd0fsQY2c+yqwyw0vNIG9EDP27NQHglOOgwhx1tQG17eetJCWcVGWbJhBSEeBcuwNQweF0biBpcBzD+h3P5MIS/n6p4dzOTVnlLGXhd43nfGaXlNS0Ixp2viwjEcz6lWqMfOnRnA9kAp8Bh3zdsTHmfVe22upysbLZBn1pFBWZGvPVwAemTGbhYw8RE1XOKR2b07tdOXMeW8HjNx5Hzy7tgKq9dYFoaLq/ELmt33aAjKeLGb2vjFlNm5ByBfSKFwyw70AFb393iK5dwyuRUYf2x7OmeF+D6gVXDZ8xpsLuGFRwuEfmpJx9DBBPzlsb+eHncg42aUXuE+E1dQKOHDXTvcfF9R6Bo5RSbr40NHcaYwIy0UlE0oFNxpjPRWoeMSQiI4AR3u5r3749r70WWW1Ujbd+brj1zsq/9x8o8xpXuMTqq9riXb3qM954eiqPX13B7v0w+8O9zFiyBwN8W7yVpPjDy6E4jjF8+eUXFBUV1biv9wtfZdvPW+nQ/nj6pFzFOT28d560atmaD77YyjnxzVlVvJ9/zNlMSWkFo2JjGP6Xv/JSwTOc1K6Ubsce4LsdTZm5ohWXDkkPq2PfJ+Uqxr2cx4Tk3ZzZKYZ1mw4wpaic3unXhFWcnsI1rppEWrxK2clzZM6lZ7QhWo4ld3lM2M3PB+/TJ8a9nEfhhReGXaxKqchSY0NTRHq4/lwmItOBl4ED7vuNMav8qUhEWgB/xxo2WytjTB6Q5+2+rl27Gl+usrmHSPgyxytYZcH6cqbx+lY2kmL1tyzUHe9z82Yyrr+h9GAUc1cc5IFUodtxUPANPPHxQRLixXV1HD5dv5fu3U8n2ZVcxzOGwoJ8Vr31HDmXR5OUcJJr6PFz9Ohxrtd5j81josnNHkn/jfv5YdFP3HLI8EPr5lx52x08NHUahSkp1pXulVbv8oTcqr3LwXh9/T22ABde+BT/nDMdZ74Th+MUxk49shc8Ut4LwY4hGPGGS6xKhYPqI3NatYxj3P3TwrLh5m36xITk3fxT57grpY5SbT2aD1e73dPjbwNc4mddJwOJgLs38yRglYj0MsZs8XNfSjU4TucGzjqnOX9/dS9ZA6BnZ2u4avfjDX+7EB7N/4lLz2hT55xVb18aJqbA1Lxcr1lfU1LTePPNNH6ZPYfzgYkndOCav/yVd/NfodeZiwKefChYdE6MigQicjzwIHCiMSZNRLoDFxpj5tscmgowz8+k1157LWw/n6pPnwA4s1MMznynPQEppRqMGpc3Mcb0N8b0B4a5//bYdqu/FRlj1hljOhhjHMYYB7AR6KGNTKUsDkcim/e3Zf0Ow1knWFdz9hwAEeGC7ifw1bYKn5b78GexamMME/7+d2bNnsNyoPiee5g6/yk+LXpWFxhXKjieBgqBE123vwXusisYpbyt+7hu0wGd466UOmq+rKO52Mu2F+t6kIi8AKwAThWRjSIyzN/glGpMhmWM4ZHl0RzXJppPNwq/7qtg4044tsMJbC07hl7nX8gn69azaMk7tV4Z93Wx6rKyMm4bMoRTHnqI06KiuGHePCY8+CBPPjaDiSnRnBPfnKZNJOQLjBcW5HPT4DTOO8NB94R2nOo4vsrankpFuOOMMYuACgBjTDl+JNpTKtC8rfs4pahc1320iXtd6z49T+OmwWl67lMRrbY5mr8DTgeOEZGrPe5qAzSva8fGmOvquN/hY4xKNQruOT1TJo7l9te+YmJqDL3POIENvzXza3mXmpaHuXXs4cWqd+7cScbllzPko4/Ij47m4VdeIe3yy4HDw6j27N5ZWT5US4W4k1JkXnSAjmf9yva9Qs6yffRu9x1zXEu6hOvwM6V8tFdEjsUatICIXADsrP0hSgWPt0zvvdOv0c9aG3gmZjrr6nasKdnCFD33qQhW2xzNU4ErgbbAQI/tu4HhQYxJqUYrJTWNPn37sbSoiGfnzeTBFU4cjhP8Wt6lrsWqN27cyOVpafz1f//j323bcvfbb9OjR4/Kx7vT8nf1mLITqqVC3PNL2x3aRseWUZzWsQmxzQ6R8/5OJg7sRI4mp1CRbxTwOnCyiCwH2gOD7Q1JNXbV57hrlmnvqi8DMyxjTECWGXPzzLFQUVFBz8QWTEwp1XOfilg1NjSNMa8Br4nIhcaYFSGMSamI4W4Qep50AnEyGJCczKCjWMOspsWq161bx9QrrmD99u3MPvVU/lNQcEQD0t0jmnnRAXq3NnUmHwokd2/qt1+XEduuCQBJnaJwbj8Qsl5VpYLJGLNKRPpiXcwV4BtjzEGbw1JK1cHbMjCTs0dy4MAjXhPt1Ye3xEx67lORzJd1NEeIyBE9mMaYW4IQj1IRY2lREXOnZnJfWkyVk064DnFZ9s47vDZ4MMP276fJeefxREEBcXFxR5Rz94hm3z+OPfm/VvaIhuI5uXtT20VHU1p2kJYxTVizqQLHcTEh61VVKphEZGi1TT1EBGPMAlsCUkr5xN+M7vXhPge664DQjShSKhh8aWi+4fF3c+APwE/BCcc37nXVarN//36f9xessm4ar29lIylWgKcen8G9yc3o4YgFDD0csUxINuTMmuZ1KM3qVZ+xMC+XYqeTBIeDoSMyvZ6cghHv888/z9cjRnBJRQUvXXEFeQsX0rx58xqPX5++/dh/T3blOp1Q87EO5Ot74613MmlqJnddfAxlZdvYvreCnGXCgKQ2TMo/wPDxd9YYh/6f2RtvOMUa5s7z+Ls5cCmwCtCGplJhrKbexuJFzoDV4Zlj4azOzVlTUsqUooMhGVGkVDDU2dA0xrzkeduVTfbDoEVUjYgMxGOOaMeOHUNVtVK1+rGkhKTB7apsS4qPpdjLEJelRUV88FoeD/2hLUmDrQn+2VMzgcBdCfXGGMP0adO4f/Jk+gKHhg9nVm4uUVG+JJwOPetY5DL78Rl8+00ZFeUHqYhqRswvXRk+3nvDXKlIYoy53fO2iLQF/mVPNEfSC42BL+vWmOONpFhrKhsfn8Aq5xZ6Jh5ePmyVcx8nde7sd8y1XeQ9cOARpubl4vz3BjrHx3Pr2NH06duv1udo9/FtqO/bYJZ1i7R4/eVLj2Z13YAOgQ6kJsaYJcAS9+2uXbsOj42N9fnxWjbyytpdv69lHY5E1m7cQq+TW1VuW+vcS2JilyMe/+y8mUxIblpZttfJrbgvbS93PzjxiDme7t7Qo423vLyc0cOGcdaCBZwFDHr4Yf72t7/ZfnzrKjcoPb2yQWl3rFrW/7J21x+B9gKJdlSsF3JVuFtaVMQCH0YChcLQEZlkT80kK9W6qLympJTsgjL+dPcdAa1nQHIyA5KTKxsBzZvXudCDrZYWFfHU4zP4saQEhyPR1tdIhZ86G5oishtXGnaXLcC4oEWkVIRwn3TuS9tbZRkRb0NcnM4NnHlZTJVt23YeZM/m73n4iq4BTyywZ88eMgYN4qply3ivaVPu//e/SU2r/xxLb5n2wnEeqlLhTkSWcPicGgV0BxbZEUs4Xsi1u34tW/+yvpwn/Nnn+++9y7ycUVbynSHHsqZ4K5NzRhETc2QehFAcg0Hp6cTERDNjznSci62M7iPvC9zF4UgsW1iQz7ycUUxIbkbSkDjW/ljza2R3rFo2MGX9VWtDU0QEON0YUxK0CJSyUfUT44233ulzI889zDNn3swqy4h4+3B1OBJZt+lb+h97eNusws1kpQY+scCWLVu48soruf6zz3i1VSv+WlTEhRde6NPwDG9qyrQXrkmPlApzMzz+LgeKjTEb7QpGqUAIxnmipuQ7di71UVNG98bK/RpZuSrC4zVS4aXWhqYxxojIm8CZIYpHqZDxdmKc5Jo36evSIr4uQzIsYwxTxt9M61aHez+/3FxG7zMSqpQ72sQCX3/9NX/v35/vtmzhn4mJvFlQwCmnnOLXPtyN7y+//ILn5s3klx07mOqlQawnEqX8IyJNgPuNMf3tjkWpQApGo1CX+gh/h1+jwwMf9TVSnnzJCLJKRM6ru5hSkcXzxNi0idCzS0uyUqNZkJcb8LpSUtPonT6CnJUn8PsZv5Kz8gS6ndqdDb81q1JuTfE+EhIc9arjww8/JKdnT0Zs2cKAs85i+ccf16uROSd7JGPP28y7d7Ri7Hmb+e6bL0lsW3WZv6SEFjidznrFqVRjZYw5BFSIyDF2x6JUIDmdG0hKaFFl29GeJ6ylPvZV2aZLfYQXfY1UXWpsaIrISNef5wMrROQHEVkrIutEZG1owlMqeLyeGONjKS52BqW+c3qcy6Il7/DJuvUsWvIOYyZOZXJhGZ+u30v5IcOn6/cyubCMoSMy/d734sWLWdS/P1fu3cu/LruMZz76iA4d/M/Z5a3x3f2EaD743+Yq5bydSAoL8hky8BJ6nZnIkIGXUFiQ73f9SjVUInKB6889wDoRmS8i/3D/2BmbUkcrGA2OYRljvJ4jh2XoUh/hovI12rBPXyPlVW1DZ28BZgMpIYpFqZDyujBySWm9exT9ZQ0nmk3OnOlV5nh6W4OzNrNmzmT83//OxcbQ9JZbmPfEEzRtWp+E0t6HKt2ecgJZLxZz0kk1Jz1aWlR0OGmDzuNUypvHgB7Ay64fpRoMz/Uf60qO56uazpF6Tgkfla/RrGkUv+gkMbGLvkaqCl/W0SwORSBKhZq3E2N2QRnDx/vfo1hfR5NYoKKigol33UXXvDx6Apc/9BDjxo3DyuFVP94a3x2OaUarE7qTs/LYGk/2C/Jywy5pg1LhyBjzjN0xKBVowWoUejtHqvCSkppWr8y7qnGoraF5lojs8rJdsPIEtQlSTHWKtMVNNd7wXLDbc2Hk4kVOmrdoTRNpwuS/38GCvNw614Ky89iWlpYy+oYbSC0oYGVUFLfNncu1111X62N92e+Nt97JpKmZZKUaurQ1fPLDHrILyrj771OPOBbu57J//36czg2cNTiOioqKyvvP6tycDYvWVynnq0h63/pb1q2hxRtOsYapLiLyek13GmMGhTIYpQJNG4VH8rbki1KNSW0NzXXGmHNCFkkNdEFpFUzuhZGXFhUxd2om9yY3Iym+HWs3biHblYE2XBYedi9c/cP3P/Djz7u4+9ddFMbGkv6vfzFgwICA1FG5ZEteLl9//RW/+91pDB9f9+LLnePjWVPyMz0TD895DeUwZKUiwM/Aw3YHoZRdlhYV8ey8mZWNrrPP78fn/323wa7PXNOSLz0uu4F0HzPbKxXp6jeRK4TCcUFpLRvcsnbU/+y8mdyXFlO5FlSvk1txX9pecubNrHP5klDE614U+Zbz4Nn/bqX414NMaRbF1KlTGTBggN+LYNe2qPag9HQGpafz2muv+XwyvPmvo5mSM4qJKaWVw5CnFB0kI2vcEbHZ/f7SssEta3f9YWy3MeY9u4NQyg7ui7n3pcWQNDiOf779HQvnfUDOkI5cPLhDlXn9/uYpCFc1Lfky9j+vwqTJ9ganVIjUtrzJiyGLQimbBSM1eyDNnzOdP55xiJfynIzYcZC+HWN48Y5E3iv0L6fI0qKiyuVLPhodx9jzNjMne+RRZ4gdkJxMRtbsKsu3nJ/2J+bPmV6ZhXZpUdFR1aFUhHPaHYBSdlmQl0tW6uGM5h98tZOHB0XRucXOygznE1OimT9nut2hBkxN3yu2/bzVpoiUCr0aG5rGmAdDGYhSdgr3taDWrP2Cj+eXcE1pBQtPackzk08j+cxjfF6KpbAgn5sGp3HHrddycOcWduwuD/jJPSU1rXL5lmEZY/hv/jNVGrRzp2ZqY1M1WsaYq+2OQSm7FDudJMUfHpXg3H6ACxxNKDtwoHJbOF3cDYSavld0aH+8TREpFXq19Wgq1WiE81pQT/zzn3xXso21hwyF57fjyXtOpU1sE9YU7/NpDqR7nsjYXlt4/ZYKJqccYk5hCYWf7wSCc3L3th5nVmo0C/JyA1qPUkqp8JfgcLCm5HBCMcdxMXzsPER0TEzltnC6uBsINa0D2iflKrtDUypk6mxoikiTUASilJ1SUtOsoZ+fdOSih62hnxlZ9q4BaYzhvjFjKLvtNnoD209qy5/TOiBC5Qlr6Ii6l2KpbPQltqBl8xi6Hy9MHCDMf9cavlPXyb2wIJ8hAy+pHALryzBbr0OG4mN97oFVStWPiKSKyDci8r2IjLc7HqUAho7IJLvgcKOr92nHcPfrFfy475iwu7gbKJXfKzymlGRkzeacHufaHZpSIeNLMqDvROQl4CljzJfBDkgpu4TTWlBlZWWMGjqUixcv5msR/vzEE3TqfBLT50zHufjwGmW+JE1wOjeQNDgOMBzb/nh+2vIj3Y4TNvx8oPLkXtOi2jVlzYPaG+He1uPULLRKBZfrwvAcYACwEVgpIq/rubtxKyzIZ+6saRQ7nSR26WJLdtfKjObzZrrW2exG+q3Deey/7zI2v+q6m76uJR1I1ZchufHWOwOScd7bki+vvfbaUe9XqUjhS0PzbOD/gHkiEgU8CfzLGONtjU2l1FHauXMn119/PX2WLePD6GgGvfIKaZdfDnDECcuXE7K70dfDEUubNm0QiWfZ5z+xo7TCdYW15i8dNWXNy5kzvdYvKsMyxjA5eyQTU6jMQptdUMbw8XX3wCrV0InIKmNMj5puH4VewPfGmPWu/f4LSAe0odlIuS8WTkhuRtLgdqz90beLhcEwIDnZSxb3iZVxzp8znawxtxEfn8DQEZl1ZnwPFG8XVCe5ljcLVQxKNVR1NjSNMbuBucBcEekLPA/kishiINsY832QYzxCQ1voPJgxRFK8kRSrv2Xd6op348aNjE9J4X8bNvBV+/aMGTeO+XNymDjmNhIcDoaOqLqmpS8x3HjrnUyamsm9yRUkxcfyzfYmzF93PI/mHV4jtKa4Nqxfz1lXt6OioqJy21mdm7Nh0frKx3iLoU/ffhw48AhT83IpXuQkIcHBn+7OoHefPgF/zdwa2nshmDEEI95wijXcVW9UBqiRCdAJ+NHj9kbgfF8fvGnTJvr161dnOffnQVRU3WkefC3rzz4Btm/fTm5u3XO+gxGrv2XBvni/XPc5ndscYOy/Ds+C2r3/EDfdcD3dzzw7ZPHWVu6XX37hp+LvSIgTWsU0YcMXW7n5pv+jk6MbcXFxdcbgdDoZfsuf2b+/lObNY+nYqbPXx9UUg/sYjX7B4xiVHmLYLX/i9DOT6qz/aN4Lv/zyC1s2/eg19kh670ZSrMGMoaHHWx91NjRdQ3GuAG4GHFgLTj8H9Ab+A5wStOis+gcCA923O3bsGMzqlLLNunXryE1L46+//EJ5585cOWECrz81lQFdy3h/606++3wTY//2X/5v+BjGjb/H5/26hyxNe3wGPy4uweFIZPj4TJ+GBVkJHLbQM/HwfEtfh8AOSE72u1GslAouERkBjPB2X7Nmzdi+fXuII6q/SIoV7Il37769NG/XhPLy8sptzZtY2+uKJ1TxbipxktC2gtimURw6VE5sM+jctoJi5/oqFzm92bNnDzu3/0RCnNCyXRR7y/ZRvP5rdu06kVatWvlUv9dj1BT27dsXtGOwfft29uzZw/atG2kmFZgKw8HSMtZ/t5tdx5/kc+yh4u9x2LNnDzt/2U7ZwTKim0VzTNxxIXtO+rkQXnyaowksA6YbYz7y2L5YRPoEJ6zDjDFLgCXu2127dh0eDguCa9nglbW7fjvKvv322zw3cCA3lpYyv0cPHnv9dTL/ehPJ3Q6ydM3PTBwgJHVqxgrnIUYvnM6FF15YZdhTXTEMSk+vbPT5E+/w28cxJXskE1NKK4fATik6SEbWuCP2o6+vlg2H+sOViOwGjLe7AGOMaROAajYBnT1un+TaVskYkwfkeXtw165dzf/+9786K3H3bvvymvha1p99gjXPLd2HYY3BiNXfsmBfvEMGXsLY86ypE2D1XHy6fi85K09g0ZJ3QhZvbeV6nZnIR6PjaNpEAKuXpfyQ4eJHdvLJutrfj0MGXsLfTiun/1mHOyFqen41xeA+Rp45BT75YQ85n3Rk8Zvv1lp/Xc/NG/ex7Xv+2Zza4iceSGtKUqco1myq4N78Cva3Pob3/vt5RL13PfdZORT5ls6V3xusXBDTq8zBbUj/Z/UpC5EVr4jUWcYbX/pKhxpjhnk2MkXkIgBjzB31qlUpVWnhM8+QkpzMF6WlZLaK5UD7lnz26ac4nRt4/8vfmDhA6BnfhKZNhItPbsroPuXMnzO9cm3MPj1P8zkbrL9qyppnZzZepSKRMaa1MaaNl5/WAWpkAqwEuolIoohEY+VXeD1A+1YRKJyX7nLzut5kSalPS504nRs4s1NMlW3+LtnlbRmS7ALfsrofjR+d3zIlLary/N4zvglT0qL40fltUOsNNm/LmwVqvW4VeXzp0fwHUH3+yCwv25RSfjDGMG3SJJpOmsQlQIffx/HkrQmsKdlG9tRMYlu04dtNm0jqdPjfdN+BCs6Kb87kD74MWYIHb1nzlFJHR0Q6AM3dt40xJUe7T2NMuYiMBAqBJsCTxpgvjna/KnJZn92zyZk1jeIXnSQmdqk1AZwdqiePW+W0kseNvK/uxrDDkci6Td/S/9jD26ov2eVONLRh/XoSHA6G3z6uyvOvPEZzprsy4joYPj4wWWdrU2HglOOqbjvlOGt7JDuc6f6wpIQWOF902hOQslWNDU0RuRD4PdBeREZ53NUG6wSmlKqn8vJyRg8bxtkLFvAjcE5Ke6bdGA9Az8QWZKXC3wvhQEUTVjgPcfHJTdl3oIKfdlWwuawth8r3MDGlXeVwKF+zwSql7CUig7ByHZwIbAMSgK+A0wOxf2PMf7DyJygFhNfSXd5Ub+jFx8czfHymT+eyYRljmDL+Zlq32lttmKbVSPXMKHvW1e1YU7KFKV4uyla/oBqKJVa6dj2Ft7/7kpTfCS1ioth3oIK3vztE167dg163rwoL8pn5UBYPTLgLhyPRp6VxvC5vVsd63arhqm3obDTQCqsx2trjZxcwOPihKRVYhQX5DBl4Cb3OTAz4UFN/9r1nzx7S09NpvmABa5o2ZWHn43jgus5VyiTFx7Jr925uuu0eRr8RxeLVZWzc05RNZR14ZHk0hySapIQWVR6zbedBPv1kRVCen1IqYLKBC4BvjTGJwKXAx/aGpJS9UlLTWLTkHT5Zt56Fi/N97k1MSU2jd/qIGqd3HDGMM7FF2AzjHDNxKo+tPo6l30fxv58OsvT7KB5bfRxjJk61OzTgcCM9q88vfDQ6jrHnbWZO9sg6v1t4G4ocbsO1VejU2KNpjHkPeE9EnjbGFPu7YxF5ErgS2GaMOcO1bTpWBtky4AfgZmPMb/UJXCl/LC0qYl7OqCrrZAVqqKm3Nbi87Xv1qs+YPzuHn97/hJ/KyvmodWv+U1jI5gfvPfLqn2t+yr0TJtKz53nMnzOd6Z8dXtR6/pzplWtjAhR+vpOZ+SU8kt6MKy8K7PNTSgXUQWPMDhGJEpEoY8wyEXnU7qCUilTn9DiX+ydN9npfOA/jtM7NTzJ/znScK6zz+5iHwmdYs7uR3jVOPOZa1j1yyttQ5HAbrq1Cp7ahs48aY+4CZovIESPGjTGD6tj308BsYIHHtqXAPa55JNOAe4Bx/gatlL8W5OVWXtWEwA419bxiWtO+CwvyKfj3Y5y46Temlh3i0dZN2Nf1GHbt/K3O+Sk1zZGcnD2SCcmGpPhYHs3/ib9cYOh/9ol+nRCUUiH3m4i0At4HnhORbcBem2NSDVhhQT5zZ02j2OkksUsXn4Y/NhQ1DeNs07o1QwZegtO5wechocEQzjkQ3I30Pbt3Vm7ztZEezs9LhVZtQ2cXun7PwJpPUv2nVsaY94Ffqm0rMsa4Fyr6GCv1ulJBV+x0HjHU1N/MdDVxOjfUue9p2ffSZf0ORuw5xLyTmvPkQ6eTc1Ur5rsaglUyu37SkeHjc+u8YpiRNZucTzpy0cO/8tW2CvomJXDMMccE/PkppQIqHSgFMoECrNE9A2t9hFL15B5xM7bXFpaPbufz8MeG4ohhnBv2Mf6V39j721bGnrfZryGhgeCe8xgJU1y8ZgPWuZbKT7UNnf3M9fs99zYRaQd0NsasDUDdtwD/DsB+lKpTgsPBmuKtQZmcXtfE98WLFvHuR6vpAfzr9NbMv+tkWjZvQlyrppVXBj2v/vmahMAzwcOfhlzBht82c6zHCCE9ISgVfowxnr2Xz9gWiGoU3CNuGmviOM9hnBsWrSchwcHB6Bhm/aGMHbvLuX72dzi3H+DYlk158L7xQT0mh+c8HqD36ceH/RQX92irzIsO0Lu1OSLRklK+qHN5ExF5FxjkKvsZsE1ElhtjRtX6wNr3eS9QDjxXw/0jgBHe7mvfvj2vvfZafau2hcYbPL7GekbPPgx/+h8cF1PKL3sriGsZxfYDsaTfdM1RP9/uPS5m3Mt5TEjezZmdYli36QBTisrpnX4NI/78ZxKfecbqrkhqyYw/t+fg/t38th9Wl+ynVcu4gBzv2mI4mv03xPdCuNB4GycR2Q24p6NEA82AvQFcS1OpSofnKB6eAVXX8Mf6ZBoNZ+4Lue6LuH17dWfbziY8vvRHJg4Qkjo1YfWmQ/z1xS8pLMgP2nOt75xHu7gb6dn3j2NP/q8611LViy/raB5jjNklIrcCC4wx94lIvXs0ReTPWEmCLjXGeF0tyBiTB+R5u69r164mPT29znrcHyi+pPIOVlmwvpxpvL6VDWasAnz4eiwZ5x3k5HYH+eHXpsxeGcuFF17oNaW5P88rPT2dwgsv5J9zpuPMd+JwnMLoB+/mvTfepOczz/AbcPzQm/h+TSHOndGVKdhzlxvG3T/tiA/tQMUwduqYej83CPx7oaG+b/0tCw0z3nCJNdwZY1q7/xYRwRpKe4F9EamGzD3ixt2jCbWPdom0Xrf6cDgSmVX4X7JThJ7x1mp93Y8XslKjK6ezBMPRzHm0S0pqGvsPlPl0vlLKm9rmaLo1FZETgCHAG0dTmYikAmOBQcaYfXWVVypQFuTlMvUPbbmqz2mceeZZXNXnNKb+oW3AUpx7pmZ/ZtGbzH/yKUr/+U++i4ripIULyXtmAX2u+kuNKdjro7Agn5sGp9Gn52kMGXgJQGUMi5a802C+FCjVUBnLq0CK3bGohqlyjuKGfT4tNeHudTsnvrlHr1t4LAcSKMMyxvDl5jK6HWf18+51rVHd+4wTgprXQOc8qsbIl4bmZKAQ+MEYs1JEugDf1fUgEXkBWAGcKiIbRWQYVhba1sBSEVkjIo8fRexK+SyYyYA87dixg5svuoiVL73EwjZtuPytt7j+xhsBKwV7oBqCjT3Bg1KRSkSu9vgZLCJTgf12x6Uiz9KiIm4anFZrYpnqiePqusjpS3K7SJeSmka3U7uzbEMTvt5SzpZ9zehwQjwbfmsW1Eafu9G/umT/Ua8vWX3t7qVFRUGIWKmjV+fQWWPMi8CLHrfXA3/04XHXedk836/olAqQYCYDclu/fj339OvH8B9/pLx9e+5/5x3OOOOMgO3fU2NP8KBUBPPMMFsOOLGGzyrls8KCfOZOzSQrNZoeQ2pfO9kzcVxdQ9DdQ227NvDEcmMmTq1c/7qbazpLsBPdBGrOo7e1uydNzQRyGaRDXFWYqbNHU0ROEpFXRGSb6+clEdFlSVREGTois2qK86O4kujNypUrmdCjB8N+/JG8bt2YuXp10BqZ0DiuOivVEBljbvb4GW6MecAYs83uuFRkmT9nOlmp0fRMbBHQIa6B7HULZ0csKxaA6Sy+1nvnPdlHNbLJc+1u92uflRrNgrzcIESs1NHxJRnQU8DzwDWu2ze6tg0IVlBKBdqA5GRiYqwU584XnQHNnvbGkiX837XX0rW0lIUXX8y8N9+kTZvaE0gWFuQzf870ei8W7W+CB6WUvURkFp6pP6sxxtwRwnBUhHM6N5B0ddsq2wKRWKYxZRr1XFYskhzOJHxYUnwsxWGcVEg1Xr40NNsbY57yuP20iNwVpHiUCppgnFTmP/EEP48axRXGEPunPzF37lyaNWtW62O8DXvxN6ufe32rCcmGpPhY1jr31mvYz9E2eJVSPvvU9fsioDuH15G+BvjSloi88GUd3/37fZ9S6mtZf/bpZles/pZ1C2S88fEJrHJupmdiC6ACgFXOfcTHx3utx594+/Ttx/57sklOTq7cVlPswXh97T62wSzrdjTxWq/9Ftdrb1nl3MdJnTsH/Di41bXfhnJsQ1nWLdLi9ZcvDc0dInIj8ILr9nXAjuCFVLdIe1E03sj+orG0qIgFebkUO50kOBwMHZHJZQMGMGncOE6aPZs44HejRzNu0iTKy8spLy+vNd5p94/jjjM306L0EMXro+na/ngmJDcjZ9Y06wTvQ7x9+vbjwIFHeOjxGfy4qASHI5Fbx2bSp28/n78QLC0qqpzjk3R1W9aU/ET2pAwOHMhlgOsLRiCPb0N93/pb1q2hxRtOsYYjY8wzACLyN+BiY0y56/bjwAd2xCQiA/GYM9qxY0c7wlD1MHREJlMeupMJKdDD0YI1JaVkF5QxfHym3aGpIBs6IpPsqZlkpVo9mWtKSplSeIA/j9ZBESr8+NLQvAWYBeRiDfv5CLg5mEF50hOhspNnY6xLchM+/N8nTBx5NbeWtuaqHTuJFqHTrFmMv+UWn/f3w3df0T89itaxTSgtO8hPm3+kS4eTKC52+hXbgORkevfpA0Dz5s39fWosyMutnOMD0DOxBVmpkJN3uKGplAq4dkAb4BfX7VaubSFnjFkCLHHf7tq163B/1isNRlm764+Usu6kLzPycil5uQSHw8HI++oekWL3c7O7/oZQdlB6OjEx0cyYMx3nYmsq0Ih77mRAcrLt8dpdv5YNfll/1drQFJEmwIPGmEFBi6AO4Xgi1LLBLWt3/Z5ln503k/vSYuh2bDnbNm+k10mCo6KC3Tt28rTAPffey18zMnze77PzZtL9hGi+236InvFCy5gmnHhMBTkFG9m7uwV9e3UnPj6BoSMy/coeV5/nVlJSTI8hcURFSeV9PRwtKVlcUlmmob++WrZhvr5hbiqwWkSWAQL0Ae63NSIVkQYkJ/vduFANQ/WpQL6MkFHKDrVmnTXGHAISRCQ6RPEoZbulRUWV61N98t8VJLY9yPaft2IqhMzZB7jtJ+gmMHd4Al+s8m/Em9O5gdtTTmDyUsOnJYcoP2SY/99ylqwr47FrW/HR6DjG9trC3KmZQV8TUxePVir0XDkPzgdeAV4GLnQPq1VKKaUakjqXNwHWA8tFJEtERrl/gh2YUnZwD5Ude95mPhodx2kdonhvTTFrnPuY8I8D3LodHmsDTc5oyXUXtPN7uKvDkUiHY5qRkRJPzvvR/H7WIeZ8UMHfk2Pod9bxVqryxBZkpR59mvq6uNPYB2vJF6XUYSLyO9fvHsCJwI+unxNd25RSSqkGxZc5mj+4fqKA1sENRyl7Vc5b7NISgLvSTuTef6/nq80VJJbD7OPhQFwzMlNOYE1JKQkJDr/2784WOzElmudHdmNN8T7+OPN7+idVXZo2KT4W52JngJ6Vd+409sFY8kUpdYRRwAjgYS/3GeCS0IajVMOk2dSVCh91NjSNMZMARKSV6/aeYAellF2KnU6SBh/Oy7Ft10Eu21jBGQZejBZOjGvOXWkncmzrpkzKP+B3hj9vjbtup0az4bcyjvVYFmtNSWlIhrBG6jpiSkUaY8wI1+/+dseiVENUWJDPg/eNZ8/mL8lKjab3gBPY8Nvh5cP69O1nd4hKNTp1Dp0VkTNEZDXwBfCFiHwmIqcHPzSlAq+wIL9y/uWQgZccMQ8yweFgTUkpxhimvvwTW/OKcRj43NGJxa8soe3JF3B/UQU5K09g+Pj6ZWdNSU1j0ZJ3+GTdehYteYcxE6dWHcK6YR/ZBTqEVamGSESuEZHWrr8niMjLInKO3XEpFcnc61O32Ps9j1/ThAFdK/hl2490O7aciSn+TUUpLMjnpsFp9Ol5mtfvCUop3/kyRzMPGGWMSTDGJAB3A3ODG5ZSgec+EbnnX449bzNzskdWOYkMHZHJpPwDXD3zB758ZTP7gScccUz951zSLr+iSgPR10amu3F776gRXk9aKalpZGTNJmflCfx+xq/kfNKR4eNztadRqYYpyxizW0QuBi4D5gOP2xyTamTquugaaebPmc7ElGh27C3nnE5RtIyJ4sQ2UWz/eStJCS1wOp0+7afye0KvLSwf3c7r9wSllO98aWi2NMYsc98wxrwLtAxaREoFiftE1LNLSyvpTpeWR1zpvPD3v4d9rfnys508D+T3OJ2p/3y23o0+z8btu3e0qvGk5dnLuXBxvq5jqVTDdcj1+wogzxjzJqCZ3VXI+HLRNdI4nRtISmiB47gY1myqAKBFTBRlBw74lU298ntCYosavycopXznSzKg9SKSBSx03b4RKxOtbXxZL2j//v0+7y9YZd00Xt/KBjvWDevXc9bV7aioqKi876zOzdmwaD2lpaVs2bKFMWlp3PHNNzzdujVPvP46559/fo31+BLv3FnTmJDcjB6OWHbtOkgPRywTkg05s6bVOF+kob4XIinWYJZ1a2jxhlOsYW6TiDwBDACmiUgMvl30VSogPC+6Aq7GFOTMmR6xI2ms5bo2M6zf8UwuLGHigEN0Ow6+2dGUJ78oIyPLt6koTucGkgbHYeXnsiQltMD5otNr+cKCfObOmkax00lily6aeEipanw5ud0CtMda7+sl4DjXtpAQkYEikuf+2bt3b6iqVg2Me/6lJ3fm2G+++YbRF17IX775hnkdO3LPhx9WNjKPRrHTSVJ81cW0k+JjqyyLsrSoqHI+yE2D03j77beOul6lVNgaAhQCKcaY34A4QCdkq5Bx9/558md4aThyL9d1bOum/HVAZ7IKm3DWjEPM/l9XMrJm+9z482d9aX+H2dY1jUaphqjGHk0RaQ78FegKrAPuNsYcDFVgbsaYJcAS9+2uXbsOj42NreURVWnZyCsbrPqH3z6OKdkjmZhSSlJCC9YU72NK0UH6/uFKLu3fn+N++425p5/OjDffJCEhISAxJHbpwtofN1deOY6KimKtcy+JiV2IjY2lsCCfeTmjmJgSTdKQY1lTvJVJD48julkug9LTAxJDuJW1u34tG9yydtcf7owx+0RkG3Ax8B1Q7vqtVEi4e//c5yWouTEVKapkdHc6cSSeT94M/3sX3UuQTUg2JMXHstZprS/trUfU3TPcw2F9NnU7tpxbTt/C3/50NT17XVild9PdKJ2YEo3jslY4dx7Ohqs9oKohq61H8xmgJ1YjMw3QAeoqoKonI1haVBTU+o5IurPyBM7uey2bxo9nyG+/cerAgTz27rt06NDB733XlFjBfZW1MqPseuuk5c4o623eaFZqNAvycn3av1IqsojIfcA44B7XpmbAs/ZFpBqbus5L4cbX81/1jO71acBVfk/4pCMXPWx9T6ipR9SzZ3jXrl1s21xC/8RDHBtbcUTvpi85IpRqiGqbo9ndGHMmgIjMBz4JTUiqMfC8upc0OI41xZuZNDUTqL0nz3Mh5lYtW9M8Jtqvk4nnupEzp09n79ixJAL/u+UWXn7iCQ4e9L/TvrAgn/tH3UzbqN2YPeXs3rCN+0fdDDxV5Srrl19+Qffup5ORdfgq5+H5IIclxcdS7DEfxNux0nXBlIpYfwDOAVYBGGN+ci93olQoeFvP2fO8FE5qO/8FK96U1LTKc2ttIyncPcM9HLHs+HkrJ7aJ4quthsT2MUfMe/V6rq9l7qdSDUVtPZqV37iNMeUhiEU1Ir725Hmqnikvq88v9cqUV1FRQWZmJh+OHUtTYEd2Ng/Pm0fTpr7kxjrSg/eNpw2/kJ1yiBV3NCE75RBt+IUH7xsPHL7K+sAjeUdcZfU6H8Q1b9RNr4Qq1aCUGWMMrmwjIqJZ3FXIBaL3L1jceQt6nZlI5l+uZ8DJZV7Pf3bPeazsGd6wj737D/DlVsPkpYZh/Y4Hqs579Wfup1INSW0NzbNFZJfrZzdwlvtvEdkVqgBVw+Q1GUG1JDnVVW9wnRPf3O8GV2lpKSMGDaLo0Ud5vWlTTlq4kDETJiAi9X0q/Oj8lnv6Q7vmB/lu637aNT/IPf2t7XXxNoQpu6CMoSMyK8s0xMQNSjVii1xZZ9uKyHDgbWCezTEpFRYKC/KZOzWTsb228NHoOP5wyi7mFG7izHGfM2TmtxR+vpOkhBZ89eWXPi0dFkyew2wHPRnFxMImZKTEk3L2MUDVhmRtw5V1aoxqyGrswjHGNAllIKpx8ZqMoFpPXnVHO/Rkx44dZAwYwNDVqylr0YLZb7xB//796xM+YF11XZCXS2npfo6JgVbR0CFO2FdmOHDwIAd9GAfgbQjT8PF3VllHsyEmblCqsTLGzBCRAcAu4FQgyxiz1OawKjXU5a0CHYPG699+fS03d9Y07k1uRo+EWJau+41VGw1P/NHQ8ZhD7CorI7uwhG+2tKf84AEmJLe1femwPn370ev8C3j77bd45uFxtGvVhLKDh1hTUkp2QRnDx99JaWkpffr248CBR5ial8vXX3/F7353GreOzeTAgTLmTs0kKzWapKvbsqbkJ7InZXDgQC69+/QJeLz+lnWLpOWtGvP/WTDL1peu3aVs4UtPXnVHM/Rkw4YN/KVHD4atXs3C9u0Z+9//HlUj0/Oqa4+Toti5H3aVwq790LwZbNkNzWNqX4PdfRUza8xtAGRPn8OiJe9UaWTCkcdqVtFWbnzcyVdffslNg9OCnkRJKRUYItJERI4zxiw1xowB/g4kishXNsWjy4epsOK5JNiT723jvtSm9IoXyg/BuZ2jGNPP8NjbO6iQZnUuHRZKl156GcPH5x5OIvRJR4aPz61yPh+QnMzCxfk88EgeCxfnMyA5mQV5uWSlRtMzsYU1NDixRZ3TiJSKJPWblKbUUfKlJ686d9rxiSlWT+bqkv3kLjd1LsT86aefcs0f/0iLn39mbrdu5C5bRqdOnY4q/vlzpleeHK46U3j4PRjTF8orDL/sFx7+oClR0a1qfLw/CX48j9XnT35J26idPH7jcVx8egdWObeQPTWTGD+TIimlQktE/g94AtgrIt8BDwBPAiuBG+yIKRyXD7O7fi0b3LJ1lUvs0oW1G3+iZ2ILireX0bNzU0rLwFDBN1sP0aFtDM1iW3Ja9+61Lh3m5plAMD4+gaEjMv1eOsxzHw5HYpVlSzwNSk/3ed/uGEtKiukxJI6oqMPTd3o4WlKyuITmzZtXKevPfu0qa3f9Wjb4Zf0VkQ3NSOtm1ni9l+3Tt1+VRtX+/ftr3a/n0JPiRU5at4rjrnuy6dO3X40x/+fNN1l2ww1cV1bGuksvZdZzz9GmTZsay/v6vDasX89ZV7WlosJwye9i6dBqP7OWV7CiuIILu7Uk5ZxjiP2l6xH1uG/PnTWNCcnNXOtvmSrDfnqdf4HX596nbz9uGpzG2F5b6JnYwnpcQiz3Jhtm1DJcyN/n5i3eQOy3obxvj7asW0OLN5xiDVMTgHONMd+LSA9gBTDY1dhTSmFdUM6elEFWKiQcG80KZxkdWhmaNovGVBziqy0VHH/88VUuPDuOOTzn0fPCc/ULuvW5MBvsrLehnhpTWJDP3FnTKHY6SezSpcZGs1KBEvZDZ3Voj/LkHnry/sqvuPOe7Fp7QOc/8QRrhwzh/LIy9l59NS+//DJt2rQJSBwJDgdrSqwv3se2P57uHaO4o28TLujaijFXdmLp99G1DgP2HB7k5suwn/o+TilluzJjzPcAxphVwHfayFSqqpTUtMohqGu3tyTzdVi7yXBCqwr2lAn//PAge3/bClC5Lna/f+zxut7lERnbXcNS/UkgGOys76Fc07Qyc3+vLSwf3c6WBEqq8Qn7Hs1wHNqjZYNb9mj3aYzh3nvvZe1DDzEA+H70aB6dNIkWLVocuYN6xjD89nE8MCmDrNRSejiOYU3JAca9sZ3fKloy49MTGXmf96uE7v0mdulSZdgPUDnsp7bhMkc+roK1xaVHDBc6mucW7LJ2169lg1vW7vrDWAcRGeVxu63nbWPMIzbEpFTYGZCczIDkZGJjY+l7/tk8+dn3TH+/HMdxMYy64niObd2UnDnTK5dlee2110j3MmS1pnWqnYudPscS7PUva1vT1JdRL/5wN5qtkVQcsdanUsEQ9g1NpfxRVlbGHddfz0cvvcSXUVFc/fjjjLjxxoDXk5KaxoEDueTk5VKyuASHoxuTH8vz+cO6+nzTNcX7jhj248vjVjn3kV1Qxsj7An/1UykVUHOB1rXcVkpVU7pvF2+P+R1Nmxyew1h+yPjU0Kspu70/w1JDMbQ1JTUtJA29w41mU7ktUI1mdxb+kpLiWuexqsZHG5qqwdi5cycZaWlcu2IFB2NimPbKK6SlBf6qoJvnVVd/1fcqZvXHxcfHM3x8pn6gKxXmjDGT7I5BqUhzNA29+l6Y9ZzH2KLVMYx/5Tem/sG/i8LhyH0s3T2aEJhGszsLf1ZqND2GBH4eq4ps2tBUDcLGjRu5s39//vL99zzTti2j3nqLc8891+6wqmSra9WyNc09khDU9yqm5+OC1YhWSiml7Fbf0T9Qvwuz7nmME5KbkTS4HWt/3M/t/zKML4hm1+5fq1wUjjTuYzkh2ZAUH8ta55EJlOrDMwt/VJTokFxVhTY0VcRbu3YtV6SlwU8/0SQhgZx33w1axraaeEt/DlTJVvfBF1vJ1at8SimllE9qG/3j6+P9uTDrbR7jrP+DnJXH8tZHn9f7eYSDymM5axrFLzpJTOwSkEaz07mBpKvbVtkWyHmsKrIFraEpIk8CVwLbjDFnuLbFAf8GHIATGGKM+TVYMaiG7+233mLRwIHcuH8/y3v35vFXXyUuLq7uBwZQTenPd5a34uEroiuH/JwT35yJrZrpVT6lGjERaWKMOWR3HKpx8nVNyHASqjmMENx5jOEgJTWtcim0QCVYczgSWVPyk2vZNUswl2hRkSWYy5s8DaRW2zYeeNsY0w1423VbqXp59513WJqSwiX797Nj0CCKiopC3siEmtOf/+j8lqSEqplukxJa4HQ6Qx6jUipsfCci00Wku92BqMZlaVGRtbzFeZv5aHScLm/hhTWPcV+Vbdpoqt2wjDFkF5Tx6YZ9QV+iRUWeoDU0jTHvA79U25wOPOP6+xngqmDVrxouYwwPPPAA6/7xDxwVFay9/XYef+WVymVBQs3p3OC1QVlh0BOWUqq6s4FvgXki8rGIjBCRwCzwq1QtFuTlBnVNyIagcl1LbTT5zHPt09/P+NXrmqaq8Qr1HM3jjTGbXX9vAY73VkhERgAjvN3Xvn17XnvttSCFFxwab+AcOnSIZ2fNwvnuu6wBTr7lFi6/9FKWLLFv3fNWLVvzwRdbOSf+cEN3dcl+2nfoyLiXf2VC8m7O7BTDuk0HmFK0h97p14T1MfYUKXFCZMUKGm9jZYzZjbW0yVwR6Qs8D+SKyGIg2xjzva0Bqgar2OkkacixVbY1pGGhgRCseYwN3dFk4VcNm23JgIwxRkRMDfflAXne7uvatavxtjBvde5J37686YNVFqhxIeFQxRBJ8dZVbs+ePWQMGsRN775LUdOmpIwezUMPPWRLrJ5lm8dEk5s9komtmlVmxctdbpgyYzYA/5wzHWe+k1Yt4xg3dVqdJ6yG+l6IpFiDWRYaZrzhEmu4E5EmwBXAzVj5Ch4GngN6A/8BTrEtONWgJTgcrCneGtQ1IRuCYMxjVOHDc/maxC5dImKeciQLdUNzq4icYIzZLCInANtCXL+KUFu2bGHkpZcy/Msveb5VK/5aVMS2beHx9qkrK57792uvvaYfZkqp74BlwHRjzEce2xeLSB+bYlKNwNARmUzOGVWvpUKUagiOXL5G1/wMtmAmA/LmdeBPrr//BOhYrHpYWlTETYPT6HVmIkMGXtLgJ/J//fXX/P6CC1j+5ZfMO/FE7v3sM3bt/I2ZD2WFzTFISU1j0ZJ3+GTdehYteUc/sJRSNRlqjBnm2cgUkYsAjDF32BeWasiWFhWxIC+XbzbtYej8LZwzeZPOpVONTmXyxsQWOk85RILW0BSRF4AVwKkislFEhgFTgQEi8h1wmeu28kNhQT5zp2YytteWRpE17sMPPySnZ0+GFhcT36sXc1avZsP6H5iTPZKsPr80imOglGpQ/uFl26yQR6EaDc/vDV9MOokFwzqS2LGlDhlUjU5NyRt1NYDgCdrQWWPMdTXcdWmw6mwMpk8ez8gzttBq/yGKN8TQrf3xTEyJbpBrMy5etIiPrr+eKw8d4vXLLuOdV1+lZcuWlVekusaJxxUpGuQxUEo1DCJyIfB7oL2IjPK4qw3QxJ6ojuTLovb79+/3eX++lvVnn252xepvWTe74p07axr3JjejR0IsUWLo4YhlQrIhZ9a0yrmI3vgbr7vXtNjpJMHhYOiITAYkJ/sVq79l6xurXWXdGlq8kRJrfHwCq5xb6JHgnntbwSrnPuLj42t8nN3HNpgx1Cdef4V66Kw6CoUF+Xz3zZf073KI3x3fhI4tDrJtcwmJbQ82uKsxubm5PHrttZx+6BAf3nIL8/LzadnSSmCgV6SUUhEoGmiFdYG3tcfPLmCwHQGJyEARyXP/7N27144wVJAVO50kxVdNapMUH0txsTNgdSwtKqrsNV0+uh1je21h7tRMlhYVBayO+sZ10+A0+vQ8jVuuH8Tbb79lazzKXkNHZFZd83PDPrILyhg6ItPu0Bos27LOKv/NnzOd7idE8+32Q/SMh5YxUZzYBpb+bzMOx/l2h3dU3FnAnBs2cGhfOU2Kf+IzYOCUKTz8978jIpVlrQWVN9M17vDjIylzXmFBPvPnTMfp3IDDkajDl5RqBIwx7wHvicjTxphiu+MBMMYsASrXhuratetwf7JsBqOs3fU3xLKJXbqwduNP9ExsQVSU1b+w1rmXxMQutT7WnxienTeT+9JiKjPa9jq5Ffel7SVn3kwGeWSs9vd5+Xq+9LbfwoJ85uWMYmJKNElDjmWV82eyHx5H61atfD7nhsPr+/577/r8ncHueO2uv66yg9LTiYmJZsasaRS/ZC1fM/I+376DhftzC1VZf/1/e3ceH1V193H884OwoyKKxY0MGPWp1YqIWqoiqGTRQqrFtUoVhNbiAiqoRVDBtgjU1IVHDaACaquCiGAhQdG6QBVEBLfWChNAwYVWHgmQgJznj5mBBBIyk8zk3pv5vl+veZGZ/Obeb4bMnJx7zz1HZzQDJBxezfU5hzJmgWPpmp3s+N7x0ZeOMfODvZhwbBawG076gh83+S+3l3zB6cCtw4dx64gRlTqZsHtB5ffWbAvcgsqxn3X4Ket1falIGjGzP0e/fMjMXtzz5mU2adgGDB5W+SxOCtrMVIw0qmt7uWvil06tIpfZdGzJyFz/TPxSNH8eF/c+e5+TGi4oLtbfDEmWk5vH9BnzeH3Jx5q8sR4E8oxm0MYzJytvhw6ZHLz/Bn7T63DG/f1rSr4pp23rxrRsfzTdz+pR5X5qm3df11okut2aaic9eC/Xn9GIB59cx9UlW3m+qdHlsiNY+ME7Vf5M3c/qQVnZfYz540i++9tGMjNDXDN8aFJeg1T/Lkx68F7uyG5Cl1ALoOprZfyUN5nvtSBlTWVtTEPL66esPjU9+u8ET1NI2snJzaOsrIBxhQWsmbFmryW49lQ0fx73/3Ekv79jSNyjbmIjjZK5RmfFjiKQ8HwM4fBqOvdtW+mxzh1aEJ4RrnWmZIl1okflNKVz37YsL6l6mY1phQV1eg1EvOb7jqaZ9QZ6x+63b9/ewzTe6jdoKGPGDmVEdhOmX3sUK9ZtY8z8cobddk9S9xO71mJkblM69z2Q5Ws2MGbsUKCgUmczWf71r08ZvPQb/vtVObZfY+647Wj+59DmPP6ncLXP6ZWdjQOyU5AnlUrCYTr3PbDSY507tKDkubA3gUSkXjjn3o3++/fYY2Z2IHCkc26FZ8EkLfTKzqZXdnaNQ+RiHaCR3cs480c/qLYDtKcBg4cxesx1SV2js8qOYmZLwnG2l1V2ftds9cVlNvF2okvCYTpffFCl5ybyGoh4zfcdTT9eQ+JVbX2NLY/3WotEt1tV7ZIlSzg6/CVdd3zPX49szp9uOoojD27O0lU1Xz+SjP3Xd23HTp1YsbZyw1fdtTJ+yJuO13Cotm61Xu/f78zsNaAPkfb3XeArM3vLOXfTPp8oUg9qO6t75HsPMW7ieMLPhWs8axqPup4l3bPzuywcmfjluju9v8wm3k50ZijE8pIvk3qmWKQ+6RrNgKmPseX1Navr3DlzmHrGGfxqx/c8u18zftntQIY+WcKJt63gikfCnHhaj6TuL1HxXD+RqNj1pUtXlQbu+lIRSYoDnHP/B1wITHPOnUZkXWkRz9Wl/c/JzePZOQt5Z+WqpPx9Utf2Mic3j8EjH2LckkP56YT/Mu6d9gy8rcAXQ04jnegtlR6rqgPZb9BQ/c0ggeb7M5pS/1JxrcWeHn30USZfey03OEfRJZdwwQ+PZebUcdzcfQcnntec9dvacN+8qRR1PcWTRiHe6ycSlYqjviISKBlmdihwMTDC6zAiFflpVvdktJc5uXm76uO5Lr6+xDvUuFd2Ns2a6W8GCS51NGUvqbjWIsY5x13DhzN/wgSWAqvuuIOHRo/mkj7n8OCvMndNv34s0Lp1adIveI93qvS6TkKwLxUbPhFJO6OBIuAt59wSM+sEfOpxJhFgd/s/9PQyztzPJbX9r43atJdBWEIskU60/maQIFNHU/aSqrNu5eXl3HD55Zw5cyblZgyaNIkBAwYA0eE6F7apVJ/sC94TOUtZ10kIRESq4px7Dniuwv1VwC+8SySyW6z9H3PXrWye91/fnkGr2Jls3Wo/mjdrSk5u3j7b+djM7n6hDqSkA3U0pUrJ/gDctGkTQ3/xCy5ftIi/NW1Kn1mzyDvvvF3fD4U6snxNZEHpmGQP10nkLGV9DB8WkfRjZkcADwKnRx96A7jRObfOu1Qiu+Xk5rGtrJz8PSb/q+pMoRedtz07k298+CUF0c7kvtp5v3U0vVA0fx6THryXknCYjp06+fJsb30KwtnvoNNkQJJy69ato9e55zJ/0SKmtWnDNYsWVepkgv8WlNakPSKSIo8DLwKHRW9zoo+J+Fasczf8lPUsuqUtw09Zz8Qx17GguLjes1TsTGY0Nk7q0JxROU13dRjqYzLDINr1f3jqBt665cBd/4fJmOgwiBYUF1f5O52ur0eqBPKMZkNb6DyVGeKtXVBczLTCAj755GOmFxbQb9DQfa6ZGe92V65cSUFeHlf/5z8UHnssY154gczMzL1ek+5n9eC7m+/lj1MeYN1za8nMDHHN8KGUlZXT9/welITDZIZCe+VK5LXt0CGTZeENlc6aLgtvoUOHDru2E6vtflYPysruY2xhASXPhnfl6X5Wj71qExGE34WKkpk3SFlTWRvT0PL6KavPtXPOVexYPmFmQ7wKIxKP6s4Uji1Mzfra+7KvS1s0Gql6u5eu2c7a8L9pVV5O/x9lMH70bWl5Fm9aYUHK5uKQ3Xx/RtPMeptZYexWWlrqdaQGZ0FxMZPGDmX4qRt47YbWDD91A5PGDq3zkcpXFy5k8llnccV//sM/OnfmlVdeITMzs9r6c845l8eefpHXl3zM9BmRI0qxXG/dcmCdc/UbNLTyWdPVkTW1+g0aWmV9r+zsXUvJTJ8xr94bUxFpkDaa2RVm1jh6uwLY6HUokX2p7kxhSUm43rPsa2kQjUaqXji8mo5ttvP1+rW0b7Wd/2mfQc+O3/PpPz9Ky7N4JeGwzn7XA9+f0XTOzSEytAiArKysgX5YELwh1T45+X7uzGtG106t+Pbbbzn1qNbcmVfKuMn302ePazTi3e706dOZcPXV3P7998w8/3wenT6dAw88MKGsFXMBVeZK5DXok59Ps2ZNmTBxPOEZkUmOrruz6vH4fv8/C3Kt1/tXbWprvd5/APQnco1mAeCARcDVniYSqUF1ZwozM0O12l5dro3bc2b899Zso+AtV2HSoqonM/TT8iZeCIU68sYHb9Mry2jZrBEGfPoNHHdoZNhxup3FywyFWF7ypc5+p5jvO5qSWkXz5/HO24tpdtz3fPbv5rRo2Zo2bdrUeoZV5xz33n03s+++mxXAsiFDePCee2jUKPGT56mY+VWzvImIV8ysMfAH51yfFGx7PNAbKAc+A652zn2b7P1Ieqpu2bNrhlc9Imhf6rpO9Z6dydat2nLrXffueq7a+aoNGDyM3w3qw2F9G3PSEY73P9/J6AWO63MO5a7isNfx6l2/QUMZPe6mlCzlJ7upo5nGYh/2PzykEdt2ODq13M66b79mU6tWfLoxI+GjOjt27OCWAQPoPG0aucDl99/P9TfcUOujiLrWQkQaEufc92aWaWZNnXPlSd78AuB259wOM7sXuB24Ncn7kDRV3ZnC2szkmox1qit2JmfPnq2OZRxycvP4w6HHMar4U/6z+XtC7ZoxOOcHHLRfBqHQodU+771l7/LU5Psb3MysvbKzadYs+Uv5SWXqaKax2If9xu8OY0zRGkb1gk5t4dX3v+CxD9sndFRn8+bNXJufz4ULF/L3jAzOeuYZLrjwwjrlq+4Iqo42iUiArQLeMrMXgV2TDjjn7qvLRp1zFS9e/wfQty7bE9lTVWcKa3MgWetUe+d3d4/lobsH89BFTekSalXj31VF8+fxxuxC7r3wwFqdffY7nf1OPXU001jswz6jsQEdGPfal3z25Vb+W7aTh6fG/yGyYcMGfnb++fxr2TLK9tuPoUVFdOvWbdf3YzParllTktDRsH1dayEiElCfRW+NgP1StI/+wDMp2rZInfhttJJf1getDzm5eZSVFTCusIA1M9bU+HfVlInjuSM7QzOzSq2po5nGKn7Y55x4ADknHsCrKzbw8MfHxP0B8sknn3BXz55ctWEDBR07cs/8+RxzzDG7vl80fx6Txg5lZG5Tulxcu2sx9GEmIg2Fc+5uADNrHb2/Od7nmtnLQPsqvjXCOTc7WjMC2AE8Vc02BgGDqvpeu3btmD17drxxPBekrKC8Mcd1OYNbny/kjuzvOOHwZqz8vIx7indwZv5Ftd5nbZ/33rJ3eWN2IXdkZ3DCuc1Y+fm/uOe2q1mcP4iTupxcq23Gw+vfhSsrzLa/ray82jwfffQhJ5zbmm+//XbXY6EDHB999KHnP0N1/JqrOkHLmyh1NNNYVUNT7ynewfCx8Q1NXbRoEU/l53NVaSlPnHACi19+mUMOOaRSzZSJ4xmZ25SuHVvSqJHVy9GwPY9OXnHNjVqaRER8wcyOB6YDbaP3vwH6Oec+rOm5zrlza9j2VcDPgHOcc66abRQChVV9Lysry+XXMNM47B4uGc9MwPHWJrJNiPxx5lXWRGtBeSvW5efnU9StGw9PHE94XphQ6BiGj919Vq0+sz41+X7uvfDAXWfseh4E+7UuZezbr3PrbbcH4rVNZe1Tk+9n5ef/ouePdx/fWrqqlOOO+1Gln8EPWSFYry0EL29t+H4dTUmdnNw8Bo98iHFLDuWnE/7LuCWHcmb+oLg6gLNmzeL6884jr7SUv557LlMWL96rkwnR4bkdKv8Cp3KdotgER8NPWc+iW9oy/JT1SVkTVEQkSQqBm5xzmc65TOBmYFJdN2pmucBwoI9zbktN9VK9ovnzuLj32Zx6Qkcu7n12Wq4xmGo5uXk8O2ch76xcxbNzFno2cslP64PGqz5/PwcMHsY9xTu0LqnUWiDPaMZz8fm2bdvi3l6qamP8nLf7WT0qXYtQXFxcY96JBQXMGjGCj4GFAwbwYEEBjRo1qvJ5HTpksiy8nq4dWwI7AVgW3kKHDh32qk/0tX1v2btMLyygJBwmMxSi36ChTCss4I7sJnQJtQAcXUItGJG9k3sfmRDXWc10/l2oSjLzBilrKmtjGlpeP2X1uVbOuVdjd5xzr5lZq309IU4PAc2ABWYG8A/n3G+SsN20sqC4mMnjbqr10hsSLMleHzTVqlsapqzsvpSM3MrJzWPx4kGMW/Km5sqQWvH9GU0z621mhbFbaWlpzU+SlNi5cycjhwxh/xEj6A2MGjmSPz3wABkZ1R+v6DdoKPcUlbF09ZbI0bDVWxgzv5x+g/a99taC4mKu7JtH964/5Mq+eXudkVxQXMwbswsZfuoG3rrlQIafuoFJY4ey8oOP9j6D2qEFa9esqfXPLSKSRKvMbKSZhaK3O4jMRFsnzrks59yRzrnO0Zs6mbUwrbBg19IbGY1jl3tEFrSXhmfA4GGMLirf64xdTX+jeKXi0jAVfz+nFRakbJ8ndTnZF2efJZh8f0bTOTcHmBO7n5WVNTCRscSqTU7t1q1buf6SS8h96SWWNGrEjyZN4pLLLqtxu32iY88nFBaw5vnIDGfX3bnvo2Gv//213UeULz6I5SVfMnrcTTRrtvuI8pOT7+eO7AxOPao1AKce1Zo780rpN+W/rFi7rdLRyRXrthAKdfTta5tutV7vX7WprfV6/wHQH7gbeB5wwBvRx8QHSsJhOl98UKXHtPRGw5XM9UHrQ3VLw5Q8G/YmkEgNfN/RFO9t3LiRPr17s3zxYkpbtuQ3c+fyk5/8JO7n98rOpld2dtx/KMazmHM4vJoTzm1W6XmdM1vSOKMZo4vKK01wNGZ+OQNv8+fRSRFJD2bWHPgNkAWsBG52zm33NpXsKTMUYnnJl75ZekNSL1nrg9aHoA31FfH90Fnx1qpVq7j2pJPot3gxBx9xBCPffpuePXumdJ/VXZxfcQKhUKgjKz8vq1SzvGQLPzzuuL0mOBp4W0G9zTqrSSREpBpTga5EOpl5gMZi+lC/QUOrHEqpyU/ED4I21FdEZzSlWkuWLOGBXr24ZtMmJh99NItefZXDDz885fuNZzHnAYOHcc9tV7Nf69JdZy5HF5Xvuki94tHJ+joyWd1F+ppEQkSA45xzJwCY2RTgHY/zSBV6ZWfTrNneQyn1GS6J2HOZtQGDk/M7FLShviLqaEqV5s6dy00XXcS927Yx/YwzmPzSS+y///4p3++C4mK+/Gojv578b0bmNuXM4w9l9bdNdnUiY/w4E1o8Q35FJG3tGibrnNsRnRlWfKiqoZQi8Ur1QecgDfUV8aSjaWZDgWuITISwErjaOdfg5rAPqsL//V+mX3cdnzrH3Cuv5LEpU2jSpEnK97uguJhJY4fyp/Ob8dWmTB4sWs+NM0s4+tjjGDbqvr0+WE/qcjJ33T065bniVd1F+ppEQkSAE83s/6JfG9Aiet8A55xL/ZE8EUk5HXQW2a3er9E0s8OBG4CuzrnjgcbApfWdQ/bmnOOZxx+nbPBgfuEcd44cyeSpU+ulkwmRaeVH5kY+nM87qQ3zbvshM2/Mou1BBwXiwzky5LfyOumaREJEAJxzjZ1z+0dv+znnMip8rU6miMcqzrFQ1bJq8YpnngmRdOHVZEAZRI7mZgAtgS88yiFR5eXl/Obiizl/9my+NGP/wkLuGj2a+hzeVRIO770GZoA+nKu7SF+TSIiIiPhXbLjr8FPWs+iWtrvW5q7NhH466CyyW713NJ1znwMTgDXAemCTc652h40kKTZt2kRebi5TZ8xgVpMmnD53Lv0HDqz3HJmhEMvXVL7OIEgfzjm5eXvNeDt4pCYCEhER8bOKw10zGhtdO7ZkZG5TpkxMfHJoHXQW2a3er9E0swOBfKAj8C3wnJld4Zx7skLNIGBQVc9v164ds2fPro+oSePnvF9//TWzRo7k8g0bWH7AAXQbOZLy7ds9yXx81+7cPquQO7I3c8LhzVj5eRn3FO/gzPyLqs3jx9f2l9fcuOvrbWXllTL6Me++BClvkLKC8oqI+EWVcyx0aEF4RjjhbVU3M6wOOks68mIyoHOB1c65rwHM7Hngp8CujqZzrhAorOrJWVlZLj8/v8adxGbgatGiRQ2VqauFyB9nfs27YsUKnhkwgCEbNzIpM5N3X3uN999/37O82dnZdOlyMg9Pvp/wvDCh0DEMH1v9h7OfX9uqpHveIGVNZS00zLx+ySoikqgql1Vbs7XWI6o0c7FIhBfXaK4BfmJmLS1yAeA5wMce5Ehrr7zyChecfjqXbNzI41278siyZb4YotorO5tn5yzknZWreHbOQn1Qi4iISErtNdx19RbGzNdwV5G6qvczms65t81sBrAM2AG8RzVnLyU1pk+dypQBA1j1/fc807cvj02fTvPmzb2OJSIiHotnPb5t2+JfjSze2kS2GeNV1kRrY9I5r9+zdj+rB2Vl9zG2sICSZ8McceSR/OrmG+h+Vo8at+31a5vK2phkvgZeZ01lhnTImyhP1tF0zt0J3OnFvtOZc457776bJnffzSXAqUOHMnbCBBo18mryYRER8YqZ9QZ6x+63b9/ewzQi3uqVnU2v7Gygfv4AF0kHnnQ0pf7t2LGDm665hpOmTmUd0LyggHFDhngdS0REPOKcmwPMid3PysoamMi1sKmo9Xr/qk1trdf7V21qa73ev2pTX5soncryULIWB67J5s2bye/Th0emTmV+kyYcP3Mmg9XJFBERERGRFFFH0yPJXBx4XzZs2MBvu3en77x5HNS2LUP+/ncuuPDCpO5DREQkHVU8YHxx77OT3oaLiARZIIfOBu3C2aryTnrwXu7IbkKXUAvA0SWzBSOyHRMevJfuZ/VISoZ//vOf/CEnh19/9RWTDj2UovnzOfroo2t8/TQZRPJrY9I5b5CyprI2pqHl9VNWkfqwoLiYyeNuYlROUzr3bcvykvWMHnMd8JBmTPdI0fx5TJk4nnB4NaFQRwYM1vqVIl7y/RlNM+ttZoWxW2lpqdeRkqIkHKZzh8pjojt3aEFJSTgp21+0aBEX9OjBL7/6ikd++EPGLV7M0UcfnZRti4iIpLtphQWMymlK106tyGhsdO3UilE5TZkycbzX0dLSXiPFTlnPxDHX6SyziId8f0bTj5MVJKO2Y6dOrFhbcXHgnawo2UrHjp3qfNH1c888w8NXXkl4+3am5Oby2PTpHHzwwXXKW5+1Xu9ftamt9Xr/qk1trdf7F6kvJeEwnS8+qNJjnTNbEn4u7E2gNDdl4vhdHX8g2vGHcRPH66ymiEd8f0azoUrV4sD3jx/Pp5deyhXbt3PdoEE89eyztGrVquYnioiISNwyQyGWl2yp9Njyki2EQiFvAqW5cHg1nTNbVnqsc2ZLwuGwN4FERB1Nr+Tk5jF45EOMW3IoP53wX8a9056BtxXU+qjbzp07ufW662g+fDgZwMYxY3jgkUfIyPD9SWsREZHA6TdoaOUDxqtKGV1U9wPGUjuhUEd1/EV8Rr0QD+Xk5u3qWMYzMUh1tm7dypVXXMELzz/PhY0b8/MnnuDyK65IVkwRERHZQ6/sbJo1e4hxE8cTfi5MKBRi8EhNPuOVAYOHMXrMdYzKiZzJXF6yhdFF5QweqY6/iFfU0Qy4jRs3MrhXL3q/9x5v7L8/177wAj179vQ6loiISINX8YCxeCvy/6COv4ifqKMZYKtWreL2Hj24Zu1aHmvXjlcWLuT444/3OpaIiIhIvVPHX8RfdI1mQC1dupRzTzuNy9euZdLRRzPhvffUyRQREREREV9QRzOA/vbSS9zdqxerv/mGR885h8lLl3L44Yd7HUtERERERAQI6NDZeCbO2bZtW9zbS1VtTDLzTnn0Ub666Sauco7MSy+l4NFHadKkSbX78DpvIrVByppobUw65w1S1lTWxjS0vH7KKiIiIt7zfUfTzHoDvWP327dv72Ea7zjnGDNiBIf9+c8cBHw8ZAgP/v73mJnX0URERERERCrxfUfTOTcHmBO7n5WVNbBFixZxP78h1JaXl9P/6qt5+umn+UWjRpzzwAPc0b+/b/PWtdbr/as2tbVe71+1qa31ev8iIiLiD77vaKa7TZs2MTgvj+zFi1nQsiX9Z8ygR48eXscSEZEGSJdOJL82Jp3zBilrKmtjGlreIGVNZYZ0yJsodTR9bO3atdzcsyfXfPYZU9u04W8vv8zJJ58c1y+liIjIvujSFBERSSV1NH1qxYoVXJiXx/gvvmByZibjXnuNUCjkdSwREWkg/Hhpitf7V21qa73ev2pTW+v1/lWb+tpEaXkTH3rl5ZcZ1q0bn33xBQ+efjqPLFumTqaIiIiIiASGzmj6zPSpU/mwf3/679zJoRdcwCNPP03z5s29jiUiIiIiIhI3ndH0CeccE/7wB7686ioyd+7k/euv57EZM9TJFBERERGRwAnkGc2gzdBUU94dO3Zw3eDBTJ8+nQuBM8aNY+R111FWVlbnDEGaAStIWROtjUnnvEHKmsramIaW109ZRURExHu+72g29FnxNm/ezNC+fen1+usUN2tG3yeeID8/3+tYIiIiIiIiteb7jqYfZ8VLVu2GDRu48Zxz6P/RRzzdujV/mTMnoTUy/fyz1aXW6/2rNrW1Xu9ftamt9Xr/IiIi4g+6RtMjn3zyCd1/8hMu+ugjphx2GDe/9RannXaa17FERERERETqzPdnNBuiN998k3vOO49/f/cdBV27Muull9hvv/28jiUiIiIiIpIUOqNZz5575hlm9uzJoO++49KcHIpfe41DDjnE61giIiIiIiJJo45mPfrzhAl8eumlnLBjB2/278+0uXNp1aqV17FERERERESSypOOppm1MbMZZvaJmX1sZt28yFFfdu7cydAhQxg6bBjvAhvHjOFPkyeTkaGRyyIiIiIi0vB41dO5H5jvnOtrZk2Blh7lSLmysjIG9enD6S+9xGEZGfxi6lQuv/xyr2OJiIiIiIikTL13NM3sAKA7cBWAc64cKK/vHPVh48aNPH777Vy/ahXPt2jBky+9RM+ePb2OJSIiIiIiklJeDJ3tCHwNPG5m75nZZDNrcBcqrlq1ijO6deNXq1YxvV07hrzzjjqZIiIiIiKSFrwYOpsBdAGud869bWb3A7cBI2MFZjYIGFTVk9u1a8fs2bPrJWhtffrpp8y/6y7+VVrKqMxMbhs1is8++4zPPvvM62hx8fvrW1GQsoLyplKQsoLyioiISMPmRUdzHbDOOfd29P4MIh3NXZxzhUBhVU/Oyspy+fn5Ne5k69atALRo0aJea+fOmUN4xAhuKC+n7VlnccGvf81ll13m27x7mj17Nl69vkHKmmgtKG+QsqayFhpmXr9klbqJvd77sm3btri3F29tItuM8SprorUx6Zw3SFlTWRvT0PIGKWsqM6RD3kTV+9BZ59wGYK2ZHRt96Bzgo/rOkQqPPvwwS/LzOa28nKJLLuGpBQto2bLBznMkIiIBZma9zawwdistLfU6kkiVFhQXc2XfPLp3/SFX9s1jQXGx15FEJA5ezTp7PfBUdMbZVcDVHuVICuccI373O/44diwXAE1uv52Hfv97zMzraCIiIlVyzs0B5sTuZ2VlDUzkzHEqar3ev2pTW1ubbRbNn8fkcTcxKqcpnS8+iOUlXzJ63E00a/YQObl5Kcuq2sRrvd6/alNfmyhPOprOueVAVy/2nWzl5eXccPnlnDJzJh0aNeL8wkIGDBjgdSwRERGRwJsycTyjcprStVNk3siunVoxKgfGTRy/q6MpIv7kxayzDcamTZu4ukcPzps5k6VNm/LInDnqZIqIiIgkSTi8ms6ZlS9D6pzZknA47E0gEYmbOpq1tHbtWs48/XRyFy/mmTZtuGbRIvLOO8/rWCIiIiINRijUkeUlWyo9trxkC6FQyJtAIhI3dTRrYeXKlVx78sl8/OGHjD/2WH7/3nucfPLJXsdqEBYUF3Nx77M59YSOXNz7bIrmz/M6koiIiHhkwOBhjC4qZ+mqUnZ871i6qpTRReUMGDzM62giUgOvJgMKrFcXLmR2375cu20bTU49lSnz5tG2bVuvYzUIC4qLmTR2KHfmNaNz37YsL1nP6DHXAQ/pOgwREZE0FGn/H2LcxPGEnwsTCoUYPHKY/i4QCYBAdjS9WnPm6aee4tNf/5qzd+5k5vnn89j06TRv3rzGPEFbI8ervI8/MoER2U3oEmoBOLqEWnBHtmPcg/fS/awevsqaaG1MOucNUtZU1sY0tLx+yioiDUtObp46liIB5Puhs35Y58s5x71jx3LNwIF8vHMnbw8cyIPPPEPz5s3rPUtDtnbNGjp3qDzFcucOLSgpCXsTSEREREREasX3ZzS9Xudrx44d3DJgAD+cNo1OwFl/+hPXXnutL9ayaWi1oVBHVqzbwKlHtd712IpwKR07dqr2uUH4uVTrr/2rNrW1Xu9fRERE/MH3ZzS9tHnzZgZkZ3PWtGl8nJHBhJkzufbaa72O1WD1GzSUMfN1wb+IiIiISND5/oymVzZs2MDPzj+f3y5bxgutW/Ob4mK6desW13VVUju9srOBAsZNvl8X/IuIiIiIBJg6mlX45JNPGHb22axYv55xHTvy4vz5HHPMMV7HSgu9srPpk5/vdQwREREREakDdTT38Oabb/JYbi6DS0tpfOKJFBYXc8ghh3gdS0REREREJDB0jWYFzz37LDN79uRnpaX89dxzeeqtt9TJFBERERERSZA6mlEPPvAAl1x6KZ/t2MGb/fszed48WrVq5XWsfSqaP4+Le5/NqSd05OLeZ1M0f15SakVEJJjM7GYzc2Z2sNdZREQkvQVy6GwyFzr//vvvueOGGzjm8cc5Fjhl9Ghuvvlmtm/fzvbt22u93YpSsTD7K6+8zNQ/3crI3KZ0vrANy9d8wZi7B1NWVhCdVCfx2lTmTWZdRQ1t0ftUZvA6b5CyprI2pqHl9VPWdGVmRwLZwBqvs4iIiPj+jKaZ9TazwtittLQ0adveunUrN1x0ET99/HFWN2rErVOmcMstt2BmSdtHqjw15QFG5jala8eWZDQ2unZsycjcpkwrLKhTrYiIBFYBMBxwXgcRERHx/RlN59wcYE7sflZW1sBkLPK9ceNG+vTpwy8XLaK4RQv6Pv88ubm5dd5ufdWuW7OWLpceRKNGuzvFXUKtWDNjzV7bSKQ2VXkTqfV6/6pNba3X+1dtamu93n+6MrN84HPn3Pv7OlhqZoOAQVV9r127dsyePTtFCZMvSFnB27zvLXuX14te4Kuvv+SQdj+ge87POanLyft8TpBe3yBlBeVNpSBlheDlTZTvO5qpsGrVKm7q2ZNla9aw4YgjeGbWLH70ox95HSshmaEQy0u+pGun3deRLi/ZQigUqlOtiIj4k5m9DLSv4lsjgN8RGTa7T865QqCwqu9lZWW5/DiWl4oNo46n8x9vbSLbhMgfZ15lTbQWvM1bNH8e7xY/ydi8pnQJHcHyki2MLnqKbt26VbtOdbLzNtTXNtFaaJh5g5Q1lRkaet7a8P3Q2WRbsmQJd3bpwm/XrKHXscfy+j/+EbhOJkC/QUMZXVTO0lWl7PjesXRVKaOLyhkweFidakVExJ+cc+c6547f8wasAjoC75tZGDgCWGZmVXVKJc1MmTi+8uUznVoxKqcpUyaO9zqaiDRwaXVGc+7cufztF7/govJypp9xBk++9BL7779/XJNy+E2v7GyaNXuIcRPHE34uTCgUYvDIYVUenUykVkREgsU5txLYtRZXtLPZ1Tn3jWehxDfC4dV0vrBNpcc6Z7Yk/FzYkzwikj7SpqP56COP8NvBg8nZuZOiSy7hsenTadKkidex6iQnNy/uzmIitSIiItIwhEIdWb7mC7p2bLnrMV0+IyL1ocEPnXXOceewYWy79lpO2LmTU0aN4qG//CXwnUwREZGqOOdCOpspMQMGD2PM/HKWrt6iy2dEpF416DOa5eXlDL3ySs6cOZNPzLjh0UfpP3Cg17FERERE6kVObh5lZQWMKyxgzYw1unxGROpNg+1obtq0icsuu4zer73Gm02b0mfWLPLOO8/rWCIiIiL1qld2Nr2ys7VMkIjUq0B2NGuavGfdunUMy8lhyerVfNquHc/MmkWXLl2qfd62bdvi3ncitTHxTDaUqgxByhukrInWxqRz3iBlTWVtTEPL66esIiIi4j3fdzTNrDfQO3a/fft9z9a+cuVKCvLyGPyf/1DeoQP3FRWRmZmZ6pgiIiIiIiIS5fuOpnNuDjAndj8rK2tgdUM/XnnlFf7SuzdXbN3KlC5dmPTiixx++OFx7yuRISWqTV2t1/tXbWprvd6/alNb6/X+RURExB8azKyz06dNIzc3l7Vbt/JCnz48/PLLtG3b1utYIiIiIiIiaSfwHU3nHGPvuov1v/oVXXbs4ISbb+bRWbNo3ry519FERERERETSku+Hzu7Ljh07uGXAAE6cNo11QL+CAgYPGeJ1LBERERERkbQW2I7m5s2bueSSSzj9b39jeUYGPZ55hgsuvNDrWCIiIiIiImnPs46mmTUGlgKfO+d+lshzN2zYwPXnnMObH33EsrZteX7uXLp165aaoCIiIiIiIpIQL89o3gh8DOyfyJPKy8u58aST+PWGDZQdfjgTFi7kmGOOSU1CERERERERSZgnkwGZ2RHA+cDkRJ9bum4dV2/YwKTjj2fysmXqZIqIiIiIiPiMOefqf6dmM4A/AvsBt+w5dNbMBgGDqnn68cAHce7qAGCTx7UHA994nCFIeYOUNdFa5Q1W1lTWNtS8fsh6rHNuvzhrpQIz+w74Z5zl+vxX3kS3G6SsqaxtqHmDlDWVGRpq3tq1rc65er0BPwP+N/p1D2Bugs9fmkBtoQ9qlTeB2iBlVd6U///qtQ1Y3iBl1a1ur50+/5U3xf+/em0DljdIWZU38dratq1eDJ09HehjZmHgr8DZZvakBzlEREREREQkBeq9o+mcu905d4RzLgRcCix0zl1R3zlEREREREQkNTyZDKgezfFBbSKUN1hZE61NREPNG6SsqaxNRJDyBimr1I0+/5U30e0GKWsqaxMRpLxByprKDMpbgSeTAdWFmS11znX1Oke8lDd1gpQVlDeVgpQVlDeVgpTVb4L02gUpKyhvKgUpKyhvKgUpKwQrb22zNvQzmiIiIiIiIlLPgtjRLPQ6QIKUN3WClBWUN5WClBWUN5WClNVvgvTaBSkrKG8qBSkrKG8qBSkrBCtvrbIGbuisiIiIiIiI+FsQz2iKiIiIiIiIj6mjKSIiIiIiIkkVuI6mmTU2s/fMbK7XWWpiZm3MbIaZfWJmH5tZN68zVcfMhprZh2b2gZn9xcyae52pIjN7zMy+MrMPKjzW1swWmNmn0X8P9DJjRdXkHR/9XVhhZrPMrI2HEXepKmuF791sZs7MDvYiW1Wqy2tm10df3w/NbJxX+fZUze9CZzP7h5ktN7OlZnaqlxljzOxIM3vVzD6Kvo43Rh/35XttH3l9+V7zM7WtqaG2NbmC1LZCsNpXta2pk85ta+A6msCNwMdeh4jT/cB859z/ACfi09xmdjhwA9DVOXc80Bi41NtUe3kCyN3jsduAV5xzRwOvRO/7xRPsnXcBcLxz7sfAv4Db6ztUNZ5g76yY2ZFANrCmvgPV4An2yGtmPYF84ETn3I+ACR7kqs4T7P36jgPuds51BkZF7/vBDuBm59xxwE+AwWZ2HP59r1WX16/vNT9T25pkaltT4gmC07ZCsNrXJ1Dbmipp27YGqqNpZkcA5wOTvc5SEzM7AOgOTAFwzpU75771NNS+ZQAtzCwDaAl84XGeSpxzrwP/2ePhfGBq9OupwM/rM9O+VJXXOVfsnNsRvfsP4Ih6D1aFal5bgAJgOOCrGcOqyXstMNY5Vxat+areg1WjmrwO2D/69QH45P3mnFvvnFsW/fo7In/AH45P32vV5fXre82v1LamlNrWJApS2wrBal/VtqZOOretgepoAn8m8sbc6XGOeHQEvgYejw5HmmxmrbwOVRXn3OdEjlKtAdYDm5xzxd6missPnHPro19vAH7gZZgE9QfmeR2iOmaWD3zunHvf6yxxOgY408zeNrO/m9kpXgeqwRBgvJmtJfLe89MReADMLAScBLxNAN5re+StyNfvNZ/4M2pbk05tqyd8/34PWPuqtjXJ0q1tDUxH08x+BnzlnHvX6yxxygC6AA87504CSvHPKfFKomPC84k04IcBrczsCm9TJcZF1unxzZHBfTGzEUSGJTzldZaqmFlL4HdEhp0ERQbQlsgQj2HAs2Zm3kbap2uBoc65I4GhRM/O+IWZtQZmAkOcc/9X8Xt+fK9Vl9fv7zU/UNuaOmpb61cQ3u8BbF/VtiZROratgeloAqcDfcwsDPwVONvMnvQ20j6tA9Y552JHAGYQaRz96FxgtXPua+fcduB54KceZ4rHl2Z2KED0X98M6aiOmV0F/Az4pfPvIrZHEfnD6P3o++0IYJmZtfc01b6tA553Ee8QOTPjiwkWqvErIu8zgOcAX0xYAGBmTYg0LE8552IZffteqyZvUN5rfqC2NXXUttaTAL3fg9a+qm1NknRtWwPT0XTO3e6cO8I5FyJyMf1C55xvjww65zYAa83s2OhD5wAfeRhpX9YAPzGzltEjVefg08kV9vAikQ8Vov/O9jBLjcwsl8jwtD7OuS1e56mOc26lc+4Q51wo+n5bB3SJ/k771QtATwAzOwZoCnzjZaAafAGcFf36bOBTD7PsEn3/TwE+ds7dV+FbvnyvVZc3KO81P1DbmlJqW+tBkN7vAWxfX0Bta52lddvqnAvcDegBzPU6Rxw5OwNLgRVE3qwHep1pH1nvBj4BPgCmA828zrRHvr8QucZlO5EP5gHAQURm6foUeBlo63XOGvL+G1gLLI/eHvE6Z3VZ9/h+GDjY65w1vLZNgSejv7/LgLO9zllD3jOAd4H3iVz3cLLXOaNZzyAydGdFhd/T8/z6XttHXl++1/x+U9uakqxqW1Of17fv9yC1r2pbU5o1bdtWi25QREREREREJCkCM3RWREREREREgkEdTREREREREUkqdTRFREREREQkqdTRFBERERERkaRSR1NERERERESSSh1NSStm9r2ZLTezD8zsOTNrmaL9dDWzB6Jf9zCzhBbpNrO7zOzzaNbYrU01tW3M7LcV7h9mZjPq9APs3tbPzey4Wj5vVPTr66Ov99/MrGn0sTPMrKBCfTszm5+MzCIiUv/UviZG7aukA3U0Jd1sdc51ds4dD5QDv4nnSWaWkchOnHNLnXM3RO/2ABJqCKMKolljt2+rqWsD7GoInXNfOOf61mJ/Vfk5kHBDSGRB3/+Nfv1L4MfAIiAnuhDwSGBMrNg59zWw3sxOr1NaERHxitrXxPwcta/SwKmjKensDSDLzNqa2QtmtsLM/mFmP4ZdRz2nm9lbwHQzC5nZwmjdK2bWIVp3UfSI4vtm9nr0sR5mNtfMQkQa26HRo6ZnmtlqM2sSrdu/4v2amNmPzOyd6LZWmNnRwFjgqOhj46M5P4jWXxX92RaYWdjMrjOzm8zsvejP2jZaN9DMlkR/hplm1jJ6lLgPMD667aOit/lm9q6ZvWFm/1NFxmOAMufcN7GHgCZASyILK18BzHPO/WePp75ApNEUEZFgU/uq9lVEHU1JT9EjqHnASuBu4D3n3I+B3wHTKpQeB5zrnLsMeBCYGq17CnggWjMKyHHOnUik4djFORcGHmH30dM3gNeA86MllwLPO+e2VxEz1nguN7NXo4/9BrjfOdcZ6AqsA24DPotuf1gV2zkeuBA4Bfg9sMU5dxKwGOgXrXneOXdK9Gf4GBjgnFsEvAgMi277M6AQuN45dzJwC7uPqlZ0OrCswv2HgH8AHYC3gKuBiVU8bylwZhWPi4hIQKh9VfsqEpPQcAWRBqCFmS2Pfv0GMAV4G/gFgHNuoZkdZGb7R2tedM5tjX7djUiDAjAdGBf9+i3gCTN7Fng+jgyTiQx9eYFIozCwmroC59yEPR5bDIwwsyOINF6fmllN+3vVOfcd8J2ZbQLmRB9fSWTIDcDxZnYPkWFCrYGiPTdiZq2JDFF6rsI+m1Wxv0OBr2N3nHPTibxeWOS6kgeAPDPrB6wFbnbO7QS+Ag6r6YcRERFfUvuq9lWkEnU0Jd1sjR6t3KWGhqS0pg06535jZqcROYr6rpmdXEP9W9HhNz2Axs65D2raR4XnPm1mb0f39Tcz+zWwqoanlVX4emeF+zvZ/RnwBPBz59z7ZnYVkete9tQI+HbP168KW4ED9nzQzA4DTnXOjTazvwNnA3cA5wALgObR54qISPCofVX7KlKJhs6KRI68/hIi134A3zjn/q+KukVEhuIQrX8j+pyjnHNvO+dGETnSeOQez/sO2G+Px6YBTwOPJxLUzDoBq5xzDwCziRwxrWr7idqPyGQBTah8HceubUdfk9VmdlE0i5nZiVVs62Mgq4rHxxAZBgXQAnBEGuPYzITHAHH/USAiIr6n9lXtq6QxdTRF4C7gZDNbQeTC/19VU3c9cHW07krgxujj481sZXSCgEXA+3s8bw5wQWyyguhjTwEHAn/ZR66K15Ast8jEBxcDH0SHJx0PTHPObQTessiECePj/7ErGUlkiNNbwCcVHv8rMCw6ucFRRBrJAWb2PvAhkF/Ftl4HTrIKh7LN7CQA51zs2pKniQwtOh2ITbveE3iplvlFRMR/7kLtq9pXSVvmnPM6g0jaMbO+QL5z7kqvs6SCmd0PzHHOvZzAc14n8pr8N3XJRESkIVP7WuVz1L6KJ3SNpkg9M7MHiczId57XWVLoD8Bp8RabWTvgPjWCIiJSW2pf96b2VbykM5oiIiIiIiKSVLpGU0RERERERJJKHU0RERERERFJKnU0RUREREREJKnU0RQREREREZGkUkdTREREREREkkodTREREREREUmq/wdZ+n5gPjn1QQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
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    }
   ],
   "source": [
    "slope_cross, intercept_cross, _, _, _ = st.linregress(y_hat,y) # check for conditional bias with a linear fit to the cross validation plot\n",
    "\n",
    "plt.subplot(121)\n",
    "plt.plot(y_hat, y, 'o', color = 'darkorange', alpha = 0.8, markeredgecolor = 'black')\n",
    "plt.plot([ymin,ymax], [ymin,ymax], 'black',lw=2.0)\n",
    "plt.plot(np.linspace(ymin,ymax,100), slope_cross*np.linspace(ymin,ymax,100)+intercept_cross, \n",
    "         alpha = 0.8, color = 'red',ls='--',lw=1.0)\n",
    "plt.title('Cross Validation Plot: Truth vs. Estimated Value')\n",
    "plt.xlabel(yname + ' Estimate (%)'); plt.ylabel(yname + ' Truth (%)'); add_grid(); plt.xlim([ymin,ymax]); plt.ylim([ymin,ymax])\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.plot(y_hat, residual, 'o', color = 'darkorange', alpha = 0.8, markeredgecolor = 'black')\n",
    "plt.plot([ymin,ymax], [0,0], 'black')\n",
    "plt.title('Cross Validation Residual Plot: Residual vs. Estimated Value')\n",
    "plt.xlabel(yname + ' Estimate (%)'); plt.ylabel(yname + ' Residual: True - Estimate (%)'); add_grid()\n",
    "plt.xlim([ymin,ymax])\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=2.0, top=1.2, wspace=0.2, hspace=0.2); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the demonstration case, there is no apparent conditional bias in the estimates over the range of values.\n",
    "\n",
    "#### Comments\n",
    "\n",
    "Linear regression is efficient with the stats module of the SciPy package in Python. With one line of code we can build a model and get the outputs needed to make predictions and check the model. I hope this was helpful,\n",
    "\n",
    "*Michael*\n",
    "\n",
    "Michael Pyrcz, Ph.D., P.Eng. Professor The Hildebrand Department of Petroleum and Geosystems Engineering, Bureau of Economic Geology, The Jackson School of Geosciences, The University of Texas at Austin\n",
    "On twitter I'm the @GeostatsGuy.\n",
    "\n",
    "\n",
    "***\n",
    "\n",
    "#### More on Michael Pyrcz and the Texas Center for Geostatistics:\n",
    "\n",
    "### Michael Pyrcz, Professor, University of Texas at Austin \n",
    "*Novel Data Analytics, Geostatistics and Machine Learning Subsurface Solutions*\n",
    "\n",
    "With over 17 years of experience in subsurface consulting, research and development, Michael has returned to academia driven by his passion for teaching and enthusiasm for enhancing engineers' and geoscientists' impact in subsurface resource development. \n",
    "\n",
    "For more about Michael check out these links:\n",
    "\n",
    "#### [Twitter](https://twitter.com/geostatsguy) | [GitHub](https://github.com/GeostatsGuy) | [Website](http://michaelpyrcz.com) | [GoogleScholar](https://scholar.google.com/citations?user=QVZ20eQAAAAJ&hl=en&oi=ao) | [Book](https://www.amazon.com/Geostatistical-Reservoir-Modeling-Michael-Pyrcz/dp/0199731446) | [YouTube](https://www.youtube.com/channel/UCLqEr-xV-ceHdXXXrTId5ig)  | [LinkedIn](https://www.linkedin.com/in/michael-pyrcz-61a648a1)\n",
    "\n",
    "#### Want to Work Together?\n",
    "\n",
    "I hope this content is helpful to those that want to learn more about subsurface modeling, data analytics and machine learning. Students and working professionals are welcome to participate.\n",
    "\n",
    "* Want to invite me to visit your company for training, mentoring, project review, workflow design and / or consulting? I'd be happy to drop by and work with you! \n",
    "\n",
    "* Interested in partnering, supporting my graduate student research or my Subsurface Data Analytics and Machine Learning consortium (co-PIs including Profs. Foster, Torres-Verdin and van Oort)? My research combines data analytics, stochastic modeling and machine learning theory with practice to develop novel methods and workflows to add value. We are solving challenging subsurface problems!\n",
    "\n",
    "* I can be reached at mpyrcz@austin.utexas.edu.\n",
    "\n",
    "I'm always happy to discuss,\n",
    "\n",
    "*Michael*\n",
    "\n",
    "Michael Pyrcz, Ph.D., P.Eng. Associate Professor The Hildebrand Department of Petroleum and Geosystems Engineering, Bureau of Economic Geology, The Jackson School of Geosciences, The University of Texas at Austin\n",
    "\n",
    "#### More Resources Available at: [Twitter](https://twitter.com/geostatsguy) | [GitHub](https://github.com/GeostatsGuy) | [Website](http://michaelpyrcz.com) | [GoogleScholar](https://scholar.google.com/citations?user=QVZ20eQAAAAJ&hl=en&oi=ao) | [Book](https://www.amazon.com/Geostatistical-Reservoir-Modeling-Michael-Pyrcz/dp/0199731446) | [YouTube](https://www.youtube.com/channel/UCLqEr-xV-ceHdXXXrTId5ig)  | [LinkedIn](https://www.linkedin.com/in/michael-pyrcz-61a648a1)\n"
   ]
  }
 ],
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